The only type of wallpaper you can safely clean by washing is vinyl. Even with vinyl, unless the care label says it’s scrubbable, use as little moisture and pressure as you can.
To wash vinyl wallpaper, use two buckets. Fill one bucket with a warm, soapy solution made from 20ml (1 tablespoon) of multi-purpose cleaner per 5 litres (1 gallon) of water. Put warm, clean water in the other bucket and use it to rinse your sponge so that you never bring dirty suds up to the paper.
Rinse and dry afterwards. For rinsing, use a slightly damp sponge, blotting it over the area you just washed. To dry the walls turn up the radiators or use an electric fan-heater so that the work is done for you. If this isn’t possible, you can lightly towel-dry the walls.
But take care: wet paper is fragile, so press the towel against the wall to blot up moisture rather than giving the wall a quick rubdown.
With non-vinyl wallpaper, the most you can do is spot clean. To do this using dry materials, you can try to soak out the grease and grime that make your wall look dull. You will need patience.
Hold a clean, absorbent cloth, or about four sheets of kitchen towel (paper towels), against the wall, then iron the cloth or sheets on a very low heat setting. The heat loosens dirt and oil, which the towelling absorbs. Another neat trick is to rub a slice of white bread against the paper which may draw out the grease element of the stain.