Scrape away any loose paint chips or bits of plaster with a putty knife before you begin working. If the damage you're repairing is a crack in the wall, apply a piece of mesh drywall tape over the crack to reinforce it.
Scoop a small amount of Spackle out of its container with a putty knife. Apply the Spackle to the damaged area; use the knife to force the Spackle into any holes and smooth it out as much as possible. Allow the Spackle to dry completely before moving on; you will know it's dry when it turns white.
Use sandpaper to sand down any bumps or ridges in the dried Spackle until it is smooth and blends in with the rest of the wall.
Moisten a sponge with water, then wipe down the repaired area to clean up any dust that is left over from sanding.