Tub with warm water
Unplug the lamp. Stand over it and gently place one hand on top of the lampshade. Push the other hand through the opening on the top. Grab hold of the light bulb and unscrew it. Pull out the hand while holding the bulb. Push your hand again through the opening and remove the rest of the light fixture.
Take the lampshade into your arms and place it in front of you. Take a dry cloth or a vacuum brush and gently dust off the lampshade inside out.
Fill the tub with warm water and add some mild detergent into it. Pour only the detergents that are used for washing delicates. Stronger detergents can damage the silk. Add enough water to cover the lampshade when placed in the tub.
Take a soft sponge or a cloth and grab some suds with it. Apply the suds on the lampshade. Start rubbing the surface of the lampshade in gentle circular motion.
Dip the lampshade in warm soapy water. Leave it submerged for a couple of seconds. Take it out of the water and dip it in again. Repeat this process a couple of times.
Observe to see if the water is dirty. Drain the dirty water and rinse the tub. Fill the tub up with clean warm water.
Dip the lamp through the clean water to wash the detergent and the dirt out. Do this a couple of times.
Place a clean towel on the floor and put down the lampshade on it. Leave the silk lampshade to air dry. You can also take the blow drier and blow dry the lampshade.
Put the lampshade back on its fixture. Screw in the light bulb and plug in the lamp.
The silk may appear to have been deformed. It will soon take on its proper form when it dries. When in a hurry, take a brown paper bag and place the lampshade in it. Take a full cup of regular kitchen salt and pour it into the paper bag. Close the bag tightly. Stir it vigorously.
Make sure that the lamp is unplugged, to avoid the risk of an electric shock. Be careful not to tear the silk with your fingers while holding the lamp shade by its frame.