Lay your tapestry out on a table or a clean floor.
Decide on the pattern you want. Pinch the center and twist the tapestry to create concentric, circular pleats to make a spiraling pattern. Fold successive horizontal, vertical or diagonal pleats to create a striped pattern. Scrunch and wad up tapestry irregularly to create an eccentric pattern. Make a series of small twists all over the tapestry to create a pattern of multiple spirals. Use clothespins to help keep folds in place as you work.
Secure the folded tapestry with rubber bands or by tying it with string. Use multiple rubber bands or strings to ensure the tapestry will not unfold during the dying process. Remove all of the clothespins.
Prepare the tapestry for dying. Some types of dyes, such as Procion Dye, require soaking the tapestry in water and soda ash fixer. In a bucket, mix and stir 1 cup of soda ash with one gallon of water. Put on rubber gloves and dunk the tapestry in the solution until it is completely saturated. Squeeze out excess water. Other types of dyes, such as RIT Dye, only require soaking the tapestry in hot water.
Prepare your dies according to the manufacturer's instructions and put them in plastic squeeze bottles. Use masking tape and a permanent marker to label the bottles with the color.
Place the tapestry on a rack over a bucket or a tub or something else that will catch the drips.
Squirt the dyes onto the tapestry until it is completely soaked through. Be creative with your color combinations. Be careful not to overlap too many colors, as you might end up making muddy looking tones. Start with light colors and then gradually add darker colors. Follow the dye manufacturer's instructions for post-application instructions. Some dyes have to be rinsed while others need to set for a few hours.
Fill your washing machine with hot water and add a cup of Synthrapol detergent. Synthrapol is specially designed to safely wash away excess dye. Cut the string or rubber bands off the tapestry and submerge it in the hot water. Run the washing machine two times.
Dry the tapestry in the dryer. The hot air of the dryer will help the dyes set. Unfold the tapestry and iron if necessary.