Have you tried hard detergent powder? Try Shampoo and wash with soft hand warm water. I have tried this method to clean my dirty reading lamp.

If it's just dusty, try setting your hair dryer on "cool" and blow the shade clean. If it's got greasy dirt mixed in, you may need to sprinkle on some talcum powder first. Watch out, don't inhale the stuff that comes off!

Use a clean or new paint brush or if your husband has an air compressor.. that works great also...

A lint roller works well for the outside of my Stiffel lamp shades made of a smooth, thick fabric. No solution for the thin and delicate fabric interior, which is not holding up nearly as well over time.

Above someone mentions compressed air. If you think this might work get a can of compressed air fr a couple of bucks from someplace that sells computer related stuff, try it and report back here as it sounds interesting.