Large holes in drywall, where you can actually see inside need a special method to repair. For instance if your wall has a hole in it from someone who got angry or perhaps something dropped against the wall it will repair with the following steps.
1. Outline the area with a square in pencil, if you have a stud finder it will help as you will need to cut a bigger square hole in the wall.
2. if you have a drywall saw that will help you cut a nice square from stud to stud only as big as you need. Otherwise a utility knife will work but take longer.
3. once you have the square removed be sure to remove a bit from the studs so you have room to screw the new piece of drywall on.
4. for best results use some scrap wood and screw it on the inside between the studs, just cut the wood big enough so you can insert it behind the drywall and screw it to the existing drywall on the top and bottom
5. size and cut your new piece of drywall, It don't have to be perfect but the smaller the gaps the faster the compound will dry later.
6. Screw the new piece on with drywall screws (duh), make sure to screw to the middle piece of scrap lumber if you added it.
7. Use fibre tape all around the edges and on the middle screw holes.
8. Add drywall compound (preferably durabond 90 for the first coat to dry fast) and scrape and sand between coats as needed, once you have it nice and smooth all you need is to prime and paint.
9. most likely you will need to paint the entire wall to match the paint.