Dust first, removing dust will prevent streaks of dusty, wet muck on your walls. Use a hand towel to dust the texture will grab the dust and lets you cover a larger area than a hand duster.
The key to cleaning stains, fingerprints and smudges off of your walls is to try to keep them as dry as possible and don't scrub too hard, gentle.
Use an instant erasing sponge, or a barely damp cloth and some baking soda or white toothpaste to gently scour the stains and oily marks off the walls.
This spot checking should be part of your weekly cleaning to ensure that the smudges don't get too imbedded in the wall.
Pull on some gloves and open a window. Mix a half a cup of ammonia into a gallon of warm water. Use a well wrung out microfiber cloth to apply the mix to the walls. Then follow it up with a clean damp cloth to remove the solution.
Work from the bottom up so if you missed any dust or dirt it won't streak down the wall.
The good news is if you keep up on the spot checking a big washing like this is only needed once a year! Ii'm Mrs. Fixit and it's just that simple!