Mix two tablespoons of dish soap with a gallon or more of warm water. Dip a scrub brush into the mixture and scrub the furniture to remove the dirt. Rinse with clean water. Set the furniture in the sun to dry.
Sand the surface with medium-grit sandpaper. Sand enough to create a rough texture without getting to bare wood. Wipe away sanding dust with a tack cloth.
Scoop a small amount of wood putty onto a putty knife. Fill any cracks in the wood furniture with the putty. Overfill slightly. Let the putty dry. Sand the surface of the crack until it is level with the rest of the surface.
Coat the surface with oil-based primer. Have the paint store tint the primer to coordinate with the paint you will be applying. Apply a thin coat of the primer with a paintbrush. Let the first coat dry. Apply a second coat of primer. Let the primer dry overnight.
Paint the furniture with oil-based enamel paint. Apply a very thin coat of paint with a paintbrush. Let the first coat dry to the touch. Apply one or two additional coats of paint. Let the paint cure for 48 hours.