Cut a 13-inch-square piece of 3/4-inch-thick hardwood for the top of the stool, using a jig saw.
Cut two pieces of 18 1/4-inch-by-5 1/2-inch wood for the stand. The pieces will crisscross, forming an X-shaped stand.
Measure and mark 9 1/8 inches down of the long sides of the stand pieces. At that point, cut two 3/4-long, 3/4-inch-wide notches.
Smooth all the cut edges on the pieces of wood with sandpaper. Start with 80-grit sandpaper and finish with 220-grit sandpaper.
Fit the notched stand pieces together to form an "X" shape. Set the stand on the floor or on a worktable. Apply a bead of wood glue along the top edges of the stand. Center and place the stool top on the stand.
Place a weight, such as a can of paint, on top of the stool to compress the wood glue. Leave the wood glue to dry overnight.
Turn the stool upside down. Screw two L-brackets on either side of each end of both stand boards, connecting the stand boards to the bottom of the stool top.
Prime and paint the stool or treat it with a clear wood finish if you want to preserve the natural wood tone.
Apply self-adhesive furniture glides to the bottom outer four corners of the stool to prevent it from scratching the floor.