Tapestries should be hung out of direct sunlight and away from heating and cooling vents and air returns. Once a year lightly vacuum the surface using the lowest suction setting with a piece of cheese cloth or nylon stocking over the vacuum attachment to prevent pulling out any threads. Tapestries should not be dry cleaned or washed. If further cleaning is required seek the services of a professional textile conservator.
Find a Conservator on the American Institute for Conservation website.
Art Conservation Organizations on the Smithsonian website.