Wash a large sheet of muslin before dying it. When using the muslin, find or buy a sheet with a width of at least 108 inches.
Remove the muslin from the washing machine and set it aside without drying it.
Fill a large bucket with hot water and place the bucket in a location that forgives splashes of dye, such as outside or in a concrete basement.
Follow the instructions on the bottle of fabric dye you choose to use. Procion MX dyes have a history of successful use as plant-based fabric dyes that retain color after application and bleed out very minimally, but any dye designed for cellulose fabrics works well. Using the bottle's instructions, pour dye into the bucket full of hot water.
Put on rubber gloves and add the just-washed muslin sheet to the dye mixture, letting it crumple up.
Swirl the muslin around in the dye to evenly coat the dye on the fabric for a solid color backdrop. For a mottled photography backdrop, leave the muslin sheet in its crumpled position in the dye, holding it underwater if necessary and moving it as little as possible.
Wait until the sheet soaks up the full saturation of dye color that you prefer for the backdrop.
Rinse the sheet after removal from the dye bucket, according to the directions on the fabric dye bottle. Run the rinsed sheet through the washing machine to bleed out any excess dye, and then hang the sheet out to dry on a line.