When the previous owners moved out of our house, they took with them the 6 speakers that they had installed in the 100 square foot breakfast nook. This was of course contrary to the contract that said built in stuff was supposed to stay. Regardless, we had a bunch of big holes in our wall. My resourceful husband found a "how to" video on This Old House's website. We watched, paused, fixed, and watched again.
1) Cut the existing hole to a clean rectangle.
2) Put two small boards or stakes inside the hole behind the drywall. This can be done with one board if the hole is fairly small. With your hand or a string, pull the board tight to the wall and put a screw on the top and the bottom. This will give you a stable place to attach a new piece of drywall.
3) Cut a piece of drywall that is slighter smaller than your exhisting hole. Attach this by putting a screw through the drywall and into the stabilizing boards.
4) Cover the whole concoction with spackle. Smooth it out with a putty knife.
5) Let that dry overnight and then sand it smooth.
6) Add another layer of spackle.
7) Let it dry and sand the second layer smooth.
8) When you paint over the patched area, make sure that paint is a good match! If not I would suggest painting the whole wall again.