Cut around the damaged area of the wall with a sharp utility knife to remove ragged edges.
Apply a length of fiberglass mesh tape over the hole. If using tape that is not self-adhesive, apply a thin layer of joint compound to the tape to adhere it to the wall.
Coat the fiberglass tape with a thin layer of joint compound, smoothing it with the putty knife so that the tape is completely covered and the joint compound is flush with the wall. Allow the joint compound to dry. Joint compound dries to the touch in a few hours, but for best results, allow it to dry for 24 hours.
Sand the area until smooth and then wipe away sandpaper particles with a clean cloth. Reapply another thin layer of joint compound with the putty knife. Allow it to dry for another 24 hours and sand again.
Prime the repair with a quality primer. Allow the primer to dry for the time recommended by the manufacturer. Latex primer usually dries to the touch in a few hours. Then paint over the repair with a paint that matches your wall color.
Cut out a square around the damaged area with a utility knife. Discard the damaged drywall.
Cut a piece of scrap drywall into a square that fits the dimensions of the cut-out drywall.
Check behind the drywall. If the damage occurred near a wall stud, attach your square to the stud with 1 or more drywall screws as needed. If the damage is not located near a wall stud, proceed to Step 4.
Cut a length of 1-inch by 2-inch lumber to approximately 4 inches longer than the height of the hole to be repaired. Insert the lumber vertically into the hole and, holding it with one hand, drill a drywall screw through the wall into the lumber at about 1 inch above and 1 inch below the hole. The lumber will provide a support for the drywall patch.
Fit the patch into the hole and screw it to the lumber with drywall screws.
Follow the steps for applying mesh tape, applying joint compound, sanding, priming and painting as described for the repair of smaller holes.