Measure the inside of the dresser drawer. Cut two pieces of plywood 1/2-inch smaller in both directions than the drawer measurements. Slip the cut plywood inside the drawer to ensure a good fit, and trim if necessary.
Place one piece of plywood inside the drawer and set the other piece aside. Screw the legs or casters to the bottom of the dresser drawer. Make sure that the screws go through the drawer base into the plywood insert to provide extra strength and stability.
Paint the drawer, if desired.
Add 2 inches to the dresser drawer's side-to-side measurement and 1 inch to the front-to-back measurement. Cut a piece of plywood and a piece of 2-inch-thick foam to these dimensions.
Lay the fabric face down on a large, flat surface. Smooth the batting on top of the fabric. Center the foam on top of the batting and place the same-size piece of plywood on top of the foam, with the edges even.
Wrap the batting over the edge of the plywood, trim to 2 inches and staple into place. Gently pull the batting smooth along all four sides, starting in the center of each side and working toward the corners. Trim excess batting even with the corners.
Wrap the fabric over the edges of the batting-covered plywood, trim to 3 inches and staple into place. Pull the fabric taut along all four sides, starting in the center of each side and working toward the corners. Fold or gather the excess fabric at each corner neatly and staple to the plywood.
Sand the rough edges of the set-aside piece of plywood and then place it over the stapled fabric on the larger plywood with the edge even with the front edge of the lid but centered side-to-side. Attach with screws placed 2 inches in from each corner.
Place the padded lid on top of the drawer to complete the footstool.