Mix equal proportions of household bleach and warm water.
Apply from top to bottom of the piece of furniture using a paintbrush.
Repeat several times, turning the piece around and upside down. Turn for two reasons: so that the sun doesn't always hit the piece in the same spot as you're working, and so that the bleach solution doesn't always run in the same direction or collect in the same spot.
Rinse with plain water.
Allow to dry thoroughly.