Take apart as much of the stool as you can with a screwdriver. Place the loose screws in a bowl and set them aside. Cover any remaining parts that you cannot remove with newspaper and painter's tape.
Smooth down any rough spots on the wood parts of the stools with Number 1 sandpaper. Wipe down the parts with a tack cloth. Sand across the grain of the wood first with Number 00 or 0 sandpaper. Then sand the wood with the grain until it is smooth. Wipe the pieces down with a tack cloth.
Apply shellac with a paintbrush to any wood knots to seal in sticky sap. Let the shellac dry overnight. Apply one or two coats of primer to the wood pieces with a paintbrush and let them dry overnight.
Sand the stool pieces again with Number 1 sandpaper. Wipe the pieces down with a tack cloth. Paint the stool pieces with the grain in long, even strokes with a paintbrush. Tap the excess paint off the paintbrush against the paint can rim. Gently smooth out any paint strokes with the paintbrush. Let the paint dry for about 24 hours.
Reassemble the stool pieces with a screwdriver when the paint is completely dry. Remove any painter's tape and newspaper protecting pieces from the painting process. Open and close the stool a few times to make sure the moving parts do not stick together.