Interior wall repair question

Doing some light renovations, and I need to fix some water damage to the sheetrock below a window. The window has already been replaced by the previous owner, but they did a crappy job on the wall below. I probably need to cut out a section maybe 10" wide from the base of the window sill to floor. What's the best way to go about this? Should I cut wider so I can screw new material into the studs? Do I want a piece of sheetrock in there, or is there something else that will work more easily? I know I'll need to tape and mud it, but we're painting anyway, so it's not a problem on that end.

Go to center of studs either side of the damage to make attaching the panel easier.  They sell 24x24 panels at the store, or for 30% more you can get 8 of them in a 4x8 sheet.  Bonus points take your knife and slice it in the parking lot for transport.  We've even cut panels to size on the cart in the HD parking lot so we could just pull from the truck and screw them to the wall

Do you have a vibrating cutter?  Like a JobMax with a vibrating cutter head?  They rock a lot for drywall.  A sharp utility knife will do but not as well.

Doing the job right, as Patrick said, is to go stud to stud.  Not only does that make things easier for assembly, it also means one fewer surprise.  It's not "wrong" to do it with scabs of lumber behind your cuts, but I always think about the next owner.  Imagine buying a used car and finding some wiring repairs with crimp connectors and electrical tape.  Now imagine finding those same repairs done with solder and shrink wrap.  Makes you feel comfy.  Like someone loved it and maintained it right.

Pull the trim off under the sill, and pull the baseboard off or at least away from the wall.  Important side note:  Take a utility knife and cut the paint where the baseboard meets the drywall.  If you don't, you'll probably pull big sections of paper off the drywall.  Cut the drywall in the center of the studs.  If you can't find the stud center, just smash the drywall in the middle and bust it out until you find the studs.  Then you can cut a neat line on the center.  Measure, cut, replace.  

Unless your house was built in the last three weeks, expect fun customizations.  You'll likely bust out the old and replace with new and not have a single issue.  Just be aware that older houses can have some fun discoveries in the walls.

I do have a vibrating cutter, and that's what I was planning to use. The house isn't that old (1977), but I've seen enough in other places to know that all kinds of things might be hiding back there. My work might not be the prettiest, but I'm not going to do a hack job (by my standards).

I like the idea of getting a 4x8 sheet of sheetrock and cutting it in the parking lot. I need more than a 2ft piece to cover the expected gap in any case, so I'll cut it into 2x4 sections.

Ceiling paint is done as of today, so this is going to be high on the list so we can move on to the walls.

There is nothing wrong with cutting your damaged panel back to the edge of the studs outboard of the damage, then screwing a 1x2 to the stud so you can screw your patch panel to that.  For an amateur, trying to get a nice clean edge down the middle of a stud can be tough, as you run into old screws, and some will be on the side you want to remove.  

Also, buy more drywall mud than you think you will need, because you may well have to go a foot onto the good wall to get to the point that you can't see the joint.

I have 2 sheets of drywall in my basement- aren't they 4'x10'? Come on by. 

drywall is typically sold in 4x8, 10, and 12' lengths.

This whole conversation is giving me hives.  My fireplace project means I have to do some drywalling and I totally suck at it.  I put it in, tape it, mud it, sand it, feel it, and it feels flawless.  Then I put a coat of primer and paint on it and it looks like I mudded with a shovel and a broken 2x4.

In related news, never ask Curtis to do body work.

Ugh. Finish work gives me the heeby-jeebies. Our last house is minus a bathroom window because I decided I'd rather install a whole fiberglass shower wall insert rather than try to cut it just right and do everything just right on the inside. We had an exhaust fan anyway. On the outside it was asbestos shingling so we matched the decorative shutters from the other windows and just put two of them on top of the hole as if someone had just closed them and then we washed our hands of it all. The drywall should have been simple as you could use a single sheet per each section on the three affected walls, but was it simple? No it was not. Did I mention I hate finish work?

I'm sure the new owners have had plenty of time to despise me while standing in the shower and looking up at the corners.

Best of luck to you, don't forget to push some insulation in there if the last owners pulled it and were too lazy to reinstall (happened at my parents' house)

Well that escalated quickly. Pulled the trim below the window sill and found it was covered in black mold. Charming.

This led to an exploratory removal of sheetrock until I found the extent of it, which means I now have a section about 10'x4' cut away (mold was not that far, but I wanted a good foot of clear area all around before I declared it good). Doesn't look to have established itself anywhere but the inner paper of the sheetrock, but I soaked everything in a strong bleach solution just the same. I won't be able to do anything more until next weekend, so it will have ample time to dry out before I close up the wall.

Can't say I'm entirely surprised, given that it was water that caused the initial damage. Thankfully, while the wall repair was poorly done, the window was professionally replaced, so there's no more water ingress to worry about (roof is also new within the last 3 years).

Follow-up question: The affected wall has baseboard heat running its length, the back portion of which is nailed to the wall. What's the best way to get down behind that, or should I just replace the sheetrock above that line and tape it?