Remove the lock and handle.
Strip the old peeling paint from the door using a scraper. Sand the area with an electric sander or sandpaper. Fill in any cracks or dents with vinyl spackling compound. Wash the surface with soap or ammonium hydroxide.
Apply a coat of primer and then two coats of paint, allowing each coat to dry before moving on to the next. Use a brush or a roller to do this. Use the same kind of paint and primer, for example oil-based or latex, throughout.
Reattach the lock and handle once the paint has dried.