Take apart the cabinet, removing all hinges and other hardware with a screwdriver. Lay the pieces in a work area. Put newspapers on the floor to protect it.
Load the palm sander with rough sandpaper. Sand the whole surface of the cabinet and all its wood parts, removing the top layer of wood. Repeat the process with medium and then fine sandpaper, so the piece is completely smooth and clean. Wipe off the dust with a tackcloth.
Brush wood stain over a 2-foot-square section of the cabinet with a finishing brush, laying it on thickly. Let it sit for one minute. Wipe up the excess stain with old rags. Repeat for each section of the cabinets. Let the stain set for eight to 10 hours.
Apply a light, even coat of polyurethane to the cabinets, section by section, using the finishing brush. Let it set 10 hours.
Sand the dried polyurethane lightly with the fine sandpaper, by hand (not using the sander), just enough to dull the surface. Wipe off the dust.
Brush on a second coat of polyurethane. Let it dry, hand-dull it, then brush on a third layer. Let it dry for a full day. Reassemble the cabinet.