Plan your design ahead of time. Create sketches of your ideas, and experiment with using different colors on your sketches. When you have a definite plan, continue to the next steps.
Transfer your plan to graph paper. Figure out how much larger you must make the painting to fit on the muslin. For example, if the sketch is on 8-by-8-inch paper, and the muslin is 8 by 8 feet, then every inch of drawing must be enlarged to 1 foot.
Obtain a piece of thick muslin large enough to cover the entire visible area of the back wall of the theater. (Make sure you have extra material at the top.) Work in a large enough space that you can spread out the muslin. Stretch and smooth the material before painting. Place weights on the corners and sides of the muslin to hold it in place.
Fold back the extra material at the top; a couple of inches will work. Sew the very top edge to the back of the muslin. Use strong thread, such as plastic coated or double thick. You now have a loop through which you can thread rope later.
Use oil paints on the muslin. Oil-based paints will last longer than water-based paints and will give a vibrant, visible finish in any color.
Thread a rope through the loop at the top when the muslin is dry. Whether you are in a small theater or a barn, find a way to hang the backdrop against the far wall. This can be from hooks screwed into the wall, or if your play needs only one backdrop, perhaps you want to simply staple gun the muslin to the back wall. (This makes the rope unnecessary.)