I need a crash course in how to use a DSLR

The reason the second photo is blurry is because you are keeping the shutter open too long, that's why your wife's hand is moving across the frame.  Sometimes this is desirable (you generally want some motion blur in the wheels of a race car, for example), but for situations like this you generally want to avoid it.

If you're in aperture priority mode, this may be why.  What that does is it lets you select the camera's aperture and then it measures the available light and dials in a shutter speed to match.  If you've got it stopped way down (meaning an aperture with a higher number, like f/11 or something) then it's going to hold the shutter open for longer, which can result in motion blur.

As a general rule of thumb, if you're taking people of people doing normal things, you probably want to wait for a shutter speed of 1/100th of a second or faster.  There is an additional rule to avoid motion blur due to the camera shaking, but it has to do with focal length and if you're using the 18-55 lens mentioned above then 1/100th will cover it.

Additionally, the photos look "noisy".  See how the cabinet color isn't consistent across the sruface?  That's generally caused by pushing "ISO" too high.  "ISO" in this case refers to how much the signal from the sensor is being amplified, in order to act like "faster" film.  A higher ISO will let you take a picture with less available light, but it causes noise.  The ability to take high-ISO photos without tons of noise is a tech that has improved dramatically in the 10 years since the d3200 was introduced.  If you have the reference guide for the camera available, see if you can figure out how to set the ISO value and set it to 400 or 800 at most.  That should improve the noise.  A low-light indoor shot with natural light may wind up being something that the d3200 will not do as well as the pixel, due to the older sensor tech.

You may also need to adjust "white balance" in the last shot.  This is related to the "color temperature" of the light that's illuminating the scene, and is something that the camera needs to compensate for when it's rendering the picture.  One of the nice things about shooting RAW is that you can do this after the fact, rather than it being locked-in when the photo is taken.

I also agree with Cooter that it looks like the lens might need cleaning.  Has someone been smearing vaseline on it? :)

As others have said, for wedding photography you need enough batteries to last the entire event, enough memory to no run out, and a backup camera (phone would work well). Plan on at least 1k shots and about 30% of the shots being kept with rest deleted. For a wedding I would get at minimum 3 additional batteries... and between now and the wedding shoot as much as you can with it to get as familiar & comfortable with it as possible. Get enough EN-EL14a batteries for the D3200 shipped to you ASAP!

For the price below get 2, at least 2 sets to have 4 batteries and 2 chargers:

https://www.amazon.com/BESTON-EN-EL14-ENEL14a-Battery-Charger/dp/B07G8Z6N82/ref=pd_lpo_1?pd_rd_i=B07G8Z6N82&psc=1

And if you don't have enough memory for 1,000+ shots at highest resolution you will be shooting then get more. Generally can be well over 1k shots for a wedding, closer to 2k shots [because exposure bracketing to be more sure of getting the shots]. Try not to use direct on-camera flash if you can; if you don't have bounce flash and experience using it then learn to shoot indoors without flash and don't be afraid of upping the ISO.

Wedding photos are about memories and getting shots which captures the occasion - not doing a commercial product shot with max resolution and detail. Most wedding photography is shot soft for a reason. Getting lighting and the subject properly represented is most important - so spend all the time you have focusing on the fundamentals of capturing lighting and exact subject you intend. Outdoor photography is much easier than indoor photography... indoors you really need to open up the aperture and lengthen the exposure times as needed which means you really need to practice getting clear shots with subject in focus. Don't be afraid of grain from higher ISO, you will need to play with ISO to keep shutter times within a good range.

If you are the wedding photographer you have the say in getting the shot... so you have authority to do what is needed to get shots (while still being respectful of the wedding party and guests). But if you need to work your way to a certain spot for the shot go ahead as it's your job to do so. And it is a big job... will have zero time for anything else, including eating. I'd bring simple snacks and water you can carry on you. Also your phone will be your backup camera, really good backup actually. So have it fully charged and bring charger with you as well.

So to recap:

1. Get more batteries! (and memory if needed)

2. Practice as much as you can shooting indoors.

3. Learn to not use onboard flash if possible - up the ISO instead.

4. Practice as much as possible to get comfortable shooting the camera and have it become as much second nature as possible! Much better to be capable with basic setup than incapable with advanced gear...

I tried some more given a max ISO, but I was still using the flash. THis is good advice.

I did clean the lens as well

In reply to tuna55 :

Did you clean both ends of the lens? Did you clean the sensor? If that is on auto with autofocus, using a flash the image should be very sharp at least somewhere. That shot is almost uniformly fuzzy to me. 

This was shot freehand, no flash, indoors and in auto. While not perfect it is fairly crisp. You can see the focus point was actually the toy instead of the girl's face. 

Studying your shot some more, it looks like the focus point may have been the corner of the table.

There should be settings for where the camera gets its focus from. Shooting a wedding I would set it to a center point to make sure whatever you are aiming at is in sharp focus. Having the foreground and background out of focus is perfectly acceptable as long as your subject is sharp. 

Another note is that (maddeningly!), Low batteries will cause slow autofocus and flash.  So you press the button and instead of an instant snap, there's a 200ms delay, which causes you to start breathing again or otherwise move.  Make sure the battery is fully charged.  Otherwise, it's like testing on bad tires.

And yeah, please post a picture that's fully in Auto mode which will use flash inside.  That'll let us know whether the camera is capable of shooting a sharp image before trying anything tricky.

Make sure that vibration reduction is on as well, on my 12 year old lenses, these two switches need set to A:

I just realized my Nikon d3500 is from about the same era...

Make sure you're looking through the eye-piece on the back, not through the lcd.  that'll cause you to be more stable since the camera is supported by your face as well.

What Toyman! Is taking about is when you're in A or S mode, the eye piece will show you a grid of dots, one of which will have a target. That's the focus & metering point. Make sure the center dot is targeted, or use the arrows on the circle control to the right of the LCD to move the targeted point to it.

In reply to WonkoTheSane :

Using the eye piece will also make your battery last much longer.  I turn the screen off, so I didn't even think of that.

You can also think of photography in the same way as taking a precision shot with a rifle... waiting for right moment, bracing to minimize movement, maintaining trigger control and doing it between breathing/heartbeat. Follow through/finger control with the shutter button minimizes movement, as does proper bracing/holding and relaxed heartbeat/taking shot between the beats. This becomes more important the longer the exposure time needs to be... like in indoor low-light situations.

I have a D3200.  I also have a brand new Galaxy S21 Ultra that has a 108mp camera and 5 other cameras for all sorts of fun effects.

I would shoot with the 3200.  Take some with the cell phone, but here's the difference.  DSLRs manipulate mechanical things inside the camera and open a shutter/aperture to allow photons of light to hit a sensor.  Cell phones use software to compile data and combine it into what the AI THINKS you were shooting and sometimes the results are hideously dirty and awful.  Search for "panorama fails" for just one example of what I'm talking about.

This photo below was taken with my S21 Ultra.  It lit up the screen to give some ambient light on my face, and the background is a campfire.  Take note that this is at midnight on NYE, I'm on the top of a mountain in the dark, and the only light was from the fire and my screen.

Aside from how damn sexy I am, notice a few things.  The way the camera took this photo was to open the shutter for about 6 seconds and (despite having no way of preventing shake) it recorded what light was hitting the sensor, where those same colors and values were moving, trying to track them, then once it absorbed enough light, it attempted to reconstruct my features using software.  My whiskers are completely non-coherent, my eyes are uneven, and it placed random jet-black whiskers around my chin.  Overall, you can look at it and say "that's Curtis!" but as a quality picture, it isn't.  It's a bunch of noise that some software put together that looks kind of like Curtis.

A DSLR manipulates mechanical settings in the camera body and lens.  It opens the shutter and absorbs whatever it absorbs in the time and area you give it.  Take a look at even the smallest lens for that D3200.  It houses a dozen fine-crystal lens elements flawlessly aligned in a precision housing.  Your cell phone has a 15mm glass disk.  I don't care how many zillion pixels a camera has, if it doesn't have the optics to feed it quality photons, it will suck.  Kinda like those little "1080p spy cameras" that are the size of your thumbnail.  There might be 1080 lines on the sensor, but that 1/2 mm pinhole lens is going to make the resulting video look like a VHS tape you found in your attic from 1983.

For your shots on the D3200, you can go full auto.  Just put in on "Auto" (or some have a green icon) and shoot.  You also might find that Shutter Priority (usually "S" on Nikons) might be helpful if you're having trouble with light.  Try to keep the shutter speed faster than 1/20 for normal focal ranges and even faster the more you zoom in.  If you have plenty of light, you might find Aperture Priority a nice thing.  You can scroll to higher numbers (smaller apertures) to get deep focal depth in case you want to include more of the fore/background, but weddings tend to be all about the couple.  Scroll that wheel down to get F3.5 and the guests and flowers in the foreground and background just turn into fuzz.

Above all, give yourself some grace.  I'm was a photography minor in college and even I don't do weddings.  I do landscapes.  Mountains and trees don't move so you can take your time and play around.  You won't be a master, but you'll do fine.  Take the camera this week and READ THE MANUAL.  There are some "rules" that the camera makes.  For instance, on Auto there isn't much you can change.  It takes control.  Program mode is kind of nice because it does the metering part, but you can use the wheel to change that proper exposure it selects.  For instance if you meter on a race car and it says F5.6 and 1/500, you can take the photo but you'll have a car that looks like it's parked because the fast shutter will freeze things.  Instead you can scroll the wheel to go for a smaller aperture and a longer exposure so the wheels are blurred.  Bingo.  Action shot.  Same amount of light getting through, but it lets you manipulate how it gets there.  Above all, you need to know which modes allow multiple shots.  Some modes are single shot only.  That gets frustrating at a wedding.

Also, it's digital.  Stuff a big card in there and you can take thousands of shots.  When they're putting rings on each other's fingers, take 20 exposures, click the wheel one way or another a couple clicks, take 20 more.  A few more clicks of the wheel, take 20 more.

Settings; I suggest you record photos in RAW+jpg.  Most formats like tiff, jpg, or other common image files are the end result.  They are a picture.  There is a red pixel at this coordinate and a blue one at this coordinate.  A RAW image file contains all the metadata for every single pixel.  A jpg file is like a poster of a Van Gogh printed on paper.  A RAW file is Van Gogh's original painting.  We can see the brush strokes, chemically analyze the paint, use carbon dating, hey look we found DNA from his ear, yadda yadda.  If they end up being edited by a pro, having all that data separated out is super nice for editing.  You remember the scene from the Matrix where Joey Pants is looking at the green characters on a screen and he says "You get used to it.  All I see is blonde, redhead."  RAW file is the green code on the screen.  "blonde/redhead" is the jpg.  When you select RAW+jpg, it will record each frame as both a jpg for quick viewing and a RAW file for editing.

In all honesty, the manual (find one on Nikon's page I assume) has all of this stuff in it.  It's pretty clear.  You need to read the section on settings anyway.  And play with it.  Take all the photos.  See what works and what doesn't.  You'll find that spending time with it is like driving a new car.  It takes you a bit to intuitively know where the headlight switch is or the limits of understeer, but once you get used to it you'll be changing shutter speeds and apertures in no time.

The first pic I took and attached here was set in "A" and "VR", that was its auto.

I may have a line on a better camera from another friend. In the meantime I'll keep trying. I did indeed clean both sides of the lens with a glasses cleaning cloth and cleaner.

Thanks for all of the detail, I am still digesting it. Nice to see you again, Curtis!

The 3200 is good enough.   Adding complexity is probably not what you need right now.    This is why the Pixel is taking better looking photos for you.

However the prospective camera has three batteries already...

If I understand correctly, on auto the little red dot is where it make the focus. When I do that, everything is terrible. There is nothing in focus here. Here is "AUTO" and "VR on" and auto focus in all of its terribleness.

Here is the best I took, just playing around with settings.

(different subject)

and I have been using the eyepiece. Bracing against something doesn't make auto any good still.

There's a good chance that lens has been dropped and needs adjustment based on the photos taken in auto. 

it was new and we've had this trouble since new, but that doesn't mean anything really.

So a smaller denominator in the aperature size is needed for lower light, and also a slower shutter speed is needed for lower light. I mix these two variables. Right?

I read the manual (skimmed) and I am referenceing a book "David Bush's Bikon 3200". Learning slowly, but the pictures are still pretty terrible.

With auto, VR, and auto focus on, that camera should be taking great photos, something is out of spec. 

I would seriously, seriously consider shooting the wedding with your phone. Clear up some storage, grab a USB power bank and skip the DSLR. 

Yes, the DSLR is capable of better photos. Heck, I've shot covers of Grassroots Motorsports with a Nikon D40 and kit lens. But a DSLR is a tool, and you sort of need to be a photo mechanic in order to use it. You can absolutely learn how to get great photos, but you don't have the time or resources to do that before the wedding, and a wedding isn't the right place for trial and error.

Use the phone. Learn the DSLR later.

Oh, and don't shoot in RAW, either. That's the equivalent of taking the tune out of your car's ECU so you can write a better one yourself. RAW is an amazing tool: If you have the expertise and time to manually edit each photo afterwards. 300 JPEGs the day after the wedding is better than 3 RAW photos 6 months later, or 300 drab unedited RAW photos. If you shoot with the DSLR, set to JPEG highest quality, vivid color mode, and automatic white balance. 

Lots of great advice. As a former wedding videographer and a DSLR hack, my advice is to focus (pardon he pun) on one thing: focus. If shots are blurry, nothing else will matter. 

Assuming that your camera is working properly, the main reason for blurry shots is motion while the aperture is open. So how do we solve this issue? 

1. Increase the shutter speed - If the shutter is only open for a small amount of time, the likelyhood of motion is reduced. The downside is that there is less time for light to enter the camera, so shots can be darker. You can increase ISO a bit, but that can make shots grainier. Ideally, you want to find a sweet spot where ISO is not too high, aperature is as wide open as possible, and shutter speed is as high as you can get to stop the action. I tend to use aperature priority and adjust the shutter speed. 
2. Reduce camera shake - Using a tripod really helps keep the camera steady, or even a monopod. These are not really practical for a wedding though, so use the eyepiece and keep your elbow braced against your body. Or put the strap around your neck, extend the camera until the straps are tight, and use the monitor. 
3. Zoom out - Zooming way in means that shake is exaggerated and it lets less light in. Moving yourself physically closer to your subject allow you to open the open the aperature and increase shutter speed. This means that you can't be a fly on the wall, get up there, get in the aisle, get in their faces. 
4. Know your focal point - As others have said, you can use a spot focus and select where it it manually, but this can get bumped and you are boned. You HAVE to keep checking the focal point to ensure that you are locked onto what you want to be locked on to. You may also have a multi-point of 3D focus option which are often better for beginners. 
5. Check your diopter - This may sound stupid, but if you are using the eyepiece, make sure it is in focus too. There is an adjustment that allows people with glasses to shoot without them. 
6. Invest in a flash - After batteries and memory cards, a flash is the #1 thing that will help at a wedding. You can get one on Craigslist or your local Wal Mart for not that much money.  You don't need all the bells and whistles, just one that will trigger from the hot shoe. Add a cheap (even homemade) diffuser and understand what settings will allow your flash to sync. Higher shutter speeds may prevent the flash from firing. Yes, you will be that obnoxious guy in the aisle with the bright flash, but bothering Aunt Martha only lasts a few seconds, good wedding photos last for years. 

Option #2 - Just use the cellphone. Seriously, most take amazing photos. You will still have to get up-close and personal, but if you are not figuring out the DSLR, you may come away with better pictures. You can download apps that allow bracketing, RAW shots and other features. You can even buy pretty cheap frames that make the phone easier to hold and use as a camera.