Create patch matching the damaged area with a utility knife.
Cut a piece of plywood to be narrower and longer than the hole.
Screw plywood backing into place, such that it will reinforce the future sheetrock patch. All screws used should be slightly below flush with sheetrock.
Place sheetrock patch into the hole, onto the plywood.
Screw sheetrock patch into reinforcing plywood.
Use putty knife to apply joint compound or spackling paste over the seams and screws. Use multiple coats until smooth and finish achieved.