Remove the fiberglass lamp shade from the lamp. Vacuum the shade using a brush attachment to remove as much dust as possible.
Wipe the fiberglass lamp shade with a dry microfiber cloth. Moisten the cloth just slightly and wipe the shade again, using a circular motion to clean the surface evenly.
Add about 1 tsp. dish soap to 2 cups water in a large bowl. Beat the solution with an electric mixer, as if you were beating eggs, until you have soap suds you can scoop up without water. Rub the suds on the lampshade with the moist microfiber cloth, drying as you go with a dry microfiber cloth.
Clean the shade with water only if there is a thick buildup of grime or nicotine that can't be removed with the other methods; avoid this step if the shade has delicate, non-waterproof trim. Fill a tub with hot water and 1/2 cup of oxygen bleach. The water should be deep enough to fit the shade underwater completely. Submerge the shade for about 30 seconds, then pull it out of the water and wipe it with a dry microfiber cloth. Repeat, if necessary. Allow the hand-dried shade to air dry overnight.