Draw an outline around the damaged part of the wallboard using your carpenter's square and a pencil. Add an inch to the measurements of the bottom and top parts of the damaged area.
Cut the sides of the outline and mark the parts where the studs are located whenever you run across one with your saw. Measure about 3/4 inch of the stud to mark its center point. Use your utility knife to continue cutting along the line.
Cut 3/4-inch plywood scraps to about 3 inches larger than the size of the trimmed patch on the wall. Hold the plywood scraps over the hole and use drywall screws to mount them in place. Do not position the screws near the edges of the plywood scraps because they could cause the wall to crumble or split.
Apply several strips of drywall tape (self-adhesive fibrerglass) around the plywood patch, making sure that the tape is centered on the seam. Apply the drywall joint compound right across the patch with your drywall taping knife and let it dry overnight.