To patch a large hole in drywall, first find the wall studs or joists on both sides of the hole. Use a carpenter's square to draw a square or rectangular opening with 90-degree corners around the damage, making sure the edges line up with the wall studs or joists. Trace the lines with a utility knife, and cut the area with a drywall saw. Make sure the edges are smooth by removing any uneven portions with the utility knife.
If you are able to remove the damaged portion of drywall in one piece, use it as a template to cut the patch. If not, measure the hole in the wall, transfer those measurements to the new drywall sheet using a pencil and a carpenter's square, and cut the patch accordingly.
Measure 2 inch by 4 inch or 2 inch by 2 inch cleats to fit in the open space, and install them. Attach them to the wall studs or joists with 3-inch screws positioned every 4 to 6 inches. Place the patch on the cleats and secure with 1 5/8-inch drywall screws every 6 inches. First place the screws in the middle, and then work out toward the edges.
Cut fiberglass tape to match the length of each seam, plus 2 inches, and cover each seam with it. Use joint compound to cover the tape in a wide layer, making sure to feather the edges. Add a second coat, and when it is dry, sand it until smooth.