Rinse the chairs thoroughly with a garden hose. This will remove loose dirt and debris from the chair. Do not scrub the chair while doing this. Rinse to avoid adding any new stains.
Pour one gallon of warm water into a bucket. Add 3 teaspoons of automatic dishwasher detergent to the warm water and mix until the detergent dissolves. Dishwasher detergent contains a mild bleaching agent and will help to not only remove the stains but also to brighten the color of the chair.
Apply liberal amounts of the detergent/water solution to the chair with a stiff brush. Scrub the mixture vigorously into the chair paying special attention to areas with dark stains. Allow the mix to set on the chair for another 10 minutes and reapply another coat with the stiff brush, scrubbing the stains as you apply the mix.
Rinse the chair off completely with the garden hose. Dry the chair off with towels. Place the chair in the sun until completely dry.
Apply automotive paste wax to the chairs with white shop rags. Do not use standard shop rags with color dyes. The dye from these can bleed into the chair resin. Apply a small film of wax and allow the wax to dry. After the wax dries, take the wax off with a separate clean, white shop rag. This will help protect the finish from getting ground in dirt and stains.