Cut enough fabric (nylon or matting material) for the size of the mat. For a 3 foot x 6 foot size tumbling mat, cut a swatch 39 inches by 76 inches, allowing extra that can be trimmed later.
Cut your foam to the size of the mat, in this case cut it to 3 feet by six feet.
Lay down a small bead of adhesive to the nylon. Use only adhesive that will not burn or deteriorate foam or nylon.
Apply the foam to the nylon and smooth it out with your hand until it is perfectly flat across the nylon.
Cut another swatch of nylon of about the same size as your previous one and drape it over the foam. Make sure the nylon stretches across the entire mat and can touch the nylon fabric underneath on all sides.
Stitch the two nylon fabrics together along the ends using a heavy duty sewing machine. If you do not have a sewing machine that can handle this job, use a bead of adhesive around the edges of the bottom section of nylon, and glue the top section to it.