How to fix a large hole in drywall
There are hole patch kits that can be purchased at most hardware stores. If that's not an option (maybe the hole is too big?) you can take a small square of drywall that's bigger than the hole and hold it up over the hole, mark around the piece with a pencil and then cut the hole out to the outside of the line. Then take two slats of 1x3 and use screws to attach them through the wall on either side of the hole creating a backing for the patch. Once that's done apply the patch to the backers and proceed to mud and tape the seams. Here's a diagram:


If you need help with the mudding/taping process there are other q/a's on this site that cover it better than I can so I won't go into it.