Spread a drop cloth on the floor under the repair area to catch debris.
Remove loose drywall or plaster lath, using a utility knife to cut it away from the damaged area. The object is to create the most solid surface you can to which the joint compound can form a bond.
Wad newspaper and push it into the hole to provide support for the joint compound if the hole is large. The newspaper should fill the hole but be beneath the surface of the wall.
Apply joint compound over the damaged area using a 6-inch drywall knife. Work the joint compound over the punched area until it is flush with the rest of the wall. Fill in all depressions in the area created by the punch. Remove excess joint compound by holding the drywall knife at more of an angle to the wall. Allow the joint compound to dry for 24 hours.
Sand the repaired area using a drywall sanding sponge. Lightly move the sponge over the area to remove any ridges or imperfections. Apply a second coat of joint compound if there are low spots that may have appeared as a result of the drying process. Sand again and paint, using a paint brush and paint that matches the rest of the wall.