Crayon marks on painted surfaces, whether from drawing or accidental marking, are relatively easy to remove. Although they are often deeply pigmented, crayon stains are thick and waxy and tend to sit on the surface rather than permeating deep into the surface. This is a nice advantage to have in stain removal. Test all cleaning solutions and application techniques in an inconspicuous location before using them in a wider area.
Remove any excess or built up crayon wax with a blunt instrument such as a tongue depressor or plastic butter knife. Soak the tip of a clean cotton swab in rubbing alcohol. Apply the alcohol-soaked cotton swab directly to the crayon marks. Use a wicking motion and work in small sections, about two inches at a time. Use fresh cotton swabs as needed to ensure that the crayon isn't being spread around. A commercially available product that can be really handy is the Tide to Go StainPen. Follow the manufacturer's directions to flood the applicator tip with the cleaning solution containing ethyl alcohol and hydrogen peroxide. This remedy might be best suited to light-colored surfaces as hydrogen peroxide can have a light bleaching effect.
Once the waxy residue has been completely removed, rinse the area with a clean sponge dampened with water. For a more thorough cleansing, opt for a dilute sudsy solution of mild pH neutral dish liquid and water. Avoid over wetting, and allow the treated paint surface to dry. If a large area was affected, you may wish to use fans to help facilitate drying and prevent lingering moisture that could encourage mildew growth.
Caution: Never mix cleaning agents or chemicals, the result can be dangerous or deadly. Before cleaning, always test the agent on an inconspicuous location to determine its suitability and to make certain it does not damage the material. Wear appropriate clothing such as gloves and protective eyewear, and work in a well-ventilated area. Accidental inhalation or ingestion of cleaning agents can be hazardous and even fatal, particularly to pets and children.