Fill the bucket with warm water and detergent. If cleaning patio furniture, car shampoo, dishwashing liquid or any general purpose detergent will work.
Add about a quarter cup of bleach to the detergent if the furniture is white or mildewed. Wear latex gloves when using any bleach solution because chlorine can be very irritating to the skin.
Turn the furniture up side down, if possible. Grime and mildew accumulates on the underside as well. As long as you are taking the time to really wash your furniture, might as well get all the underside spots. Wash and rinse the undersides, then turn the furniture right side up and wash that side last.
Scrub the furniture thoroughly with the sponge. Use a toothbrush to get into any nooks and crannies. If the furniture is older or very inexpensive, softer plastic, do not use the scrub side of the sponge unless you really need to remove a stubborn stain. It could scratch the finish.
Rinse the furniture completely. If this can be done outside with a garden hose, all the better. Dry with a soft cloth to prevent water spots.
Finish with a coat of car wax for a water repellent shine. Simply follow the directions as for waxing a car and make extra sure to buff it smooth and dry before use.