Closely examine the nap of the fabric. The nap is the direction of the little loops that make up the entire fabric.
Brush down your stage curtains with a lint roller to remove large composites of dust and lint. Move with the nap of the fabric.
Vacuum your curtains. You may need to stand on top of a very large ladder to reach all of the curtain. Again, you must move in the same direction as the nap in order to properly hang the curtains.
Apply dry cleaning solvents to any stains you encounter. Never use chemicals like bleach to remove stains, or you may blemish the fabric.