A styrofoam ball can be covered with fabric using several different methods. You can wrap, decoupage, punch-cover and section-cover the shape for a variety of looks. Wrapping the ball simply means pulling a large piece of fabric around the shape and tying it tight. Decoupage uses small scrap pieces of fabric that are slicked over the shape with a glue and water mixture. However, the punch covering and section covering methods involve very specific steps.
Cut 10 squares from flexible fabric, 5 by 5 cm (2 by 2 inches) each. The fabric you use to cover a styrofoam ball needs to be soft and easy to fold, such as cotton or satin. It should not be stiff and rough, such as leather or denim.
Place a large dab of glue on the top of the styrofoam ball. Take a piece of fabric, and push the middle of the square against the glue and into the ball about 1.25 cm (1/2 inch) deep with the tip of a pencil. Repeat the process to glue and push another piece of fabric next to the first, making sure the styrofoam does not peek through.
Continue pushing the squares into the styrofoam ball. Cut more squares as needed to cover the entire shape -- the larger the ball, the more squares you'll need to use. Let the glue dry. The results should look like a frilly, floral ball.
Measure the size of your styrofoam ball from the middle of the top to the middle of the bottom. Cut long, thin fabric ovals the same size as the ball measurement. Cut two or three ovals to start.
Carefully secure a fabric oval to the styrofoam ball with fabric glue. Place the fabric oval vertically, so that the oval top secures to the top of the ball. Press the shape flat and smooth down the rounded ball.
Repeat this process with additional ovals, overlapping the fabric slightly at the top and bottom of the ball. Keep cutting ovals as needed and repeating the process, overlapping the fabric slightly, to cover the ball. Let the glue dry.
If you're very exact, you can cut shapes that do not overlap when you use sections to cover a styrofoam ball with fabric. Mentally divide the ball into four to six vertical shapes that look like long and skinny ovals with pointed tops and bottoms. Cut the shapes out of fabric, and cover the ball. The number of sections needed will depend on the size of your styrofoam ball.