How to use and read a caliper and micrometer the right way

Jazz hands. Okay, not really. 

Just one quick comment. You used 'accurate' and 'precise' as synonyms. In measurement, they are different concepts. Using target shooting as the analogy, accuracy measures how close to the bullseye your shots are while precision measures how close to each other your shots are.

In high school I took machine tool and we had to learn how to read a vernier caliper. 

I'll add a couple of bits to go along with this fine video.

1. Always zero your caliper each time you take a measurement. I always give the jaws a wipe, too before I zero them.  You're measuring at the 0.001" scale.  It doesn't take much to be off.  Even more so with a micrometer.
2. Take multiple measurements, especially when measuring the ID of a hole.  There's a bit of a technique to moving it around a bit to find the actual ID.
3. They said it in the video, but I'll add to it because it's always worth saying: don't crank down on anything.  There's a bit of flex in the caliper measurement system, you want the calipers to not be under any stress when taking the measurement.

The folks at the magazine probably can't link stuff in their official posts, but I'm under no such constraints.  Here's a brief video showing the different measuring surfaces on a caliper:

Starrett YouTube Video

Starrett and Mitutoyo are generally "the best" as far as measurement instruments like this go.  I personally have a bit of a preference for Mitutoyo equipment.

one note here, when measuring I.D. with calipers the jaws are not parallel thus the measurement is not as accurate as you may think. Probably ok for what you're doing but worth remembering  

I qualify in PMI (precision measuring instruments) for my job as an Outside Machinist.

We set up portable machines to half a thou or 0.0005 and sometimes a 1/4 thou. The Inside Machinists, who sit at their perfectly level lathe all day sometimes come out of their cave and shadow us. They E36 M3 a brick when we are setting up a portable machine with wooden wedges and a 3# hammer.

Depending on how you do during the PMI exam your qual can be up to 5 years before requal. I shake pretty bad but still can get the 5 year qual due to many many years of practice.

Always zero your junk out.

the video really only shows how to read the gauges.   the hard part ("skill") is in cleaning, squaring, pressure, knowing how to deal with non-flat surfaces,....and being consistent with technique.