Refer to the wallpaper's manufacturer's guidelines first. Stains should be removed as soon as possible. Do not rub spots.
Dirt spots can be removed with mild soap (castile soap) and warm water. Rinse. Blot wallpaper dry with a towel.
For tougher surface stains, use a liquid vegetable oil-based laundry detergent. Test on a small spot first, and always rinse after applying a detergent.
Crayon marks: Rub area with white toothpaste and a damp cloth. Do not use on nonvinyl wallpaper.