Keep your paper and fabric lampshades out of direct sunlight to help prevent them from discoloring and premature ageing.
Use no more than the recommended wattage bulbs in your lamps to keep the shades from scorching or burning.
Dust your lampshades lightly for cleaning. Lampshade cleaning sponges are available at your local DYI center. Some silk shades can be washed, but beware, it is a tricky task. You can end up with water spots or a rusted frame.