Depending on what dye was used to color you cloth, there are many different chemicals that will remove it. To start with, though, just try soaking and washing in hot water. That will remove loose dye. In many cases there is no need to do anything more than wash in hot water. Make sure that the water in your washing machine is at least 140°F, for maximum effectiveness.

If your cloth is 100% cotton, linen, or hemp, you can use household chlorine bleach to break apart the dye on the cloth. Don't even try bleach if your cloth is made with any synthetic content at all, though, such as spandex, nylon, or polyester. Chlorine bleach will destroy synthetic fibers. Don't use it on animal-type fibers, either, such as wool, cashmere, or silk, because they will just dissolve in bleach.

Other dye removers are gentler to the fiber and can be used on synthetics with care. Try Rit Color Remover, Tintex Color Remover, or Jacquard Color Remover. All of these work best in very hot water, and none will work well in cool water. See What chemicals can be used to remove dye? for a full discussion of different chemicals used for removing dye from cloth.

Not all dyes can be removed at all. Some dyes are resistant to all methods of color removal. You can't know whether the dyes in your cloth are removable until you try it. Some dyes can be removed with bleach but not color remover, and some can be removed with color remover but not bleach. It's a trial-and-error process.

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[This answer was first posted, by me, on Yahoo answers, on November 9, 2008.]