For silk or linen shades, start with a light dusting by a feather duster, micro cloth, or gentle vacuum to remove dirt.
Next, mix a teaspoon of very gentle detergent or Ivory soap with water in the tub or sink.
Rinse the shade gently with warm water and hang to dry.
For paper shade really stubborn stains, try using a dry cleaning sponge. Be Careful with Water: Water can easily ruin a paper lampshade. But, if it is extremely soiled or stained, wipe it with a dampened cloth or sponge that you've wrung out well.