Full answer
The repair approach depends entirely on the size of the hole. Nail holes and small dings up to about a half inch are a one-step job: fill with lightweight spackling compound using a putty knife, let it dry (usually 30 to 60 minutes for small amounts), sand lightly with 120-grit sandpaper, and paint. Lightweight spackling shrinks very little and requires only one application in most cases.
For holes 1 to 4 inches — common from doorknob impacts or anchor removals — use a self-adhesive mesh patch kit available at any hardware store for about $5 to $8. Clean the edges of the hole, stick the mesh patch over it, and apply joint compound (also called mud) in thin coats with a 6-inch putty knife. Let each coat dry fully (2 to 4 hours) before applying the next. Two to three thin coats produce a flatter, stronger repair than one thick coat.
For holes larger than 4 inches, cut the damaged area into a clean rectangle, cut a piece of new drywall to fit, and screw it to backing boards or a commercial drywall patch clip system. Tape the seams with paper joint tape, embed it in the first mud coat, then apply two additional coats feathered 6 to 12 inches beyond the patch. This method is more involved but produces a seamless, professional result.
Texture matching is often the trickiest part of drywall repair. If your walls have a light orange peel texture, a can of spray texture costs about $6 and can be dialed to match most common finishes. Apply lightly from 18 inches away, let dry, then prime and paint. The patch will be invisible under paint.