We made this using hardware-store supplies, but you could adapt the technique for an existing screen.
From the plywood, cut three 2-by-6 1/2-foot pieces.
Sink pilot holes for bifold hinges: Attach the left-hand panel to the center panel by screwing hinges 6 inches from the top and bottom, and a third in the center. Repeat to attach the center panel to the right-hand panel. Remove hinges; they will be reattached in the same holes in step 7. (If you're using an existing screen, simply remove the hinges.)
Cut 6 pieces of fabric 2 feet 1 1/2 inches by 6 feet 7 1/2 inches; press.
Place 1 panel flat, and lay a piece of batting over it. Stretch a piece of fabric over the panel, so its 4 edges just cover the edge of the plywood. Staple the top side, then the bottom, then the sides. Trim any excess fabric. Repeat with the panel's reverse side. Trim again.
Repeat step 4 to cover the other 2 panels.
Cover the staples: Using glue, attach ribbon along the perimeter of each panel.
Screw 2 stabilizing feet into the bottom edges of each panel.
2 sheets 3/4-inch birch plywood (4 feet by 8 feet)
6 bifold hinges
7 yards gingham or other check fabric, 60 inches wide