Claire, to answer your last question, you can ususally buy a damaged or partial sheet but you may have to find someone to ask about this. At about $5/sheet, it's not much of an investment and some spare drywall for checking paint colors or techniques can be handy also. Just be sure that you get the correct thickness for this job. It's probably 1/2", but check.
Now as to how to fill the hole, start by cutting/snapping a piece of drywall slightly larger than the hole. A half inch extrain both dimensions should do it for this hole. You cut drywall by scoring (cutting the outside paper) the surface and snapping it from the other side, then cut the paper on the second side.
Drill 2 holes toward the center of the repair piece and run some string through the holes, then tie the string into a loop. This will be your handle for holding the piece inside the wall. Next, put a small ridge of spackle around one face of the piece, turn and put it into the hole. Using the string, just get it in position while the spackle sets up a little. Wipe off any big smears if you can or just work the excess spackle into the corner of the old drywall and the repair piece inside the wall.
Let this set up well--a couple of hours is OK but over night is better. Cut off the string. Finally, cut another piece of drywall slightly smaller that the hole, spackle the edges and put that into the hole. You will want to fill any voids or remove any excess spackle with a putty knife. You may have to do a leveling coat of drywall, then sand flush.
Takes a little time to do this but it's more drying time than actual working time and it's an easy job.