Head for your nearest fabric or arts and crafts store to pick up 5 to 10 yards of muslin. It's easiest to find in white. A flat white king-sized bed sheet will also work.
Carefully fold about an inch of the fabric edge over and iron it flat. Following the instructions on your glue or tape, apply it to the inside of your folded edge to create a no-sew hem on all four sides of the muslin. This keeps your backdrop from fraying. Betterphoto.com recommends fusible tape for creating a clean edge.
If you want to get fancy, fold down 4 inches on one side and glue or tape to create a pocket that will allow you to slide the backdrop onto a backdrop stand.
Wash your fabric and leave it damp. Do not put it in the dryer.
Follow the instructions on the fabric dye and prepare the dye. This typically involves mixing dye into hot water with some salt.
If you want a tie-dye background, lay out the damp fabric and crumple it, beginning in the center. You are going to crumple and ball up the entire piece and wrap it in loosely in twine. You will have a messy, twine-wrapped ball of fabric when you are done. Do not tie the twine too tight. Dye needs to seep in to get the swirled look of tie-dye.
If you have a tie-dye ball, put it in the tub of dye. Stir it around with a pole or with your gloved hands until the color looks good. The outside color will be the darkest part of your tie-dye pattern.
If you are creating a solid background, put the fabric in the dye and stir with your pole to get full coverage.
For a slightly mottled or swirly look, don't stir the fabric too much. Leave it to sit for 2 to 4 minutes between stirring to keep the dye from covering evenly.
The dyeing process should take about 30 minutes.
Thoroughly rinse your background to remove the extra dye and then dry it flat. Ironing is optional.