A clean lamp shade makes a bigger difference than you'd think. Here's the most effective method, plus the mistakes most people make.
Vacuum the lamp shade with the upholstery attachment using gentle suction. This removes dust.
Roll a lint roller over fabric shades to pick up lingering dust and debris.
For fabric shades, dab stains with a damp cloth and a tiny amount of mild dish soap. Test first.
For plastic or paper shades, wipe with a slightly damp cloth and mild soap solution.
Air dry shades completely before placing back on the lamp. Damp shades can warp and grow mildew.