If your vacuum has a soft brush attachment, put it to work on your lampshades to remove dirt and hair. For pleated fabric shades, try an angled attachment and take your time. Plan to vacuum your shades at the same time you tackle your upholstery for a double dose of clean.
A feather duster or microfiber cloth may get some of the dust off your fabric lampshades, but instead, go with a lint roller or clean paintbrush to remove the dirt, pet hair and dust. In a pinch, you can even use tape to lift off dust.
If your fabric shade is stitched rather than glued, you may be able to give it a bath. Use a teaspoon or two of mild dish soap or baby shampoo in a basin of water. Remove your shade from the base and dip it into the soapy water. You can lightly swish it in the water. Follow with a clean water rinse. You can place the shade in a sunny spot to allow it to dry thoroughly.
Hopefully, you will have luck getting your shades back to near-new condition with a good cleaning. If you would like to know more about fabric lampshade care, call Lamps & Lamp Shades Specialties at 310-836-6677.