Using 100-grit sandpaper, lightly sand the damaged area. Sand 4"-6" beyond the perimeter of the hole as well. Remove any dust or debris with a lightly water-dampened rag.
Cover the hole with an appropriately sized self-adhesive wall patch and press firmly.
Using a putty knife, apply 4 inches of patching material around the perimeter of the wall patch. Allow it to dry.
Again using a putty knife, apply patching material over the repaired area and feather it 6"-8" beyond the edges. Allow it to dry.
Use 220-grit sandpaper to smooth the patched area and make it even with the surface.
Remove any final dust or debris from the finished repair.