Scrape away any loose plaster around the hole. Chipped or loose plaster will prevent the patch from adhering to the wall properly.
Widen the hole to about 1/8 inch, using a utility knife or a large tool. This gives the patch better footing to adhere to the wall.
Blow away the plaster dust.
Fill the hole with patching plaster or spackle compound, using a putty knife.
Allow the compound to dry for at least 24 hours, or according to package directions.
Sand the patched area lightly with sandpaper, paying attention to blending the edges.
Prime the patched area with a sealing coat, and paint it to match the surrounding wall.