Place the plywood panel on a work surface. Draw a 16-inch diameter circle onto the panel using a compass.
Cut out the circle from the plywood panel using a band saw. Move the panel through the band saw in a smooth motion just fast enough to allow the blade to cut through the wood.
Sand the cut edge of the plywood circle with a fine-grit sanding pad until it is completely smooth. This is the seat.
Apply edge banding around the edge of the plywood circle using a flat iron. Rub the flat iron across the surface of the edge banding in a steady motion until it adheres to the edge. Trim the edge banding to fit the seat with an edge banding trimmer.
Wipe off the seat with a tack cloth just before you are ready to apply the spray lacquer. Spray the seat with clear spray lacquer. Apply two even coats of lacquer. Allow the finish to dry four hours between coats. Wait 24 hours after the final coat before continuing.
Evenly space the three stool legs around the outside edges of the seat. Position the legs one inch in from the outside edge of the seat. Drive the screws that were included with the legs through the mounting holes into the seat using a screw gun.