Remove loose dirt and other debris from teak furniture by wiping with a slightly damp cloth. Wipe wood dry with a dry cloth.
Apply a gentle, oil-based soap such as Murphy's Oil Soap to the furniture with a soft-bristle brush. Mild soap should remove most stains. For a deeper clean to remove mold or mildew, mix one qt. of sudsy ammonia and 1/2 capful high phosphate laundry detergent such as Wisk in a five-gallon bucket, and apply to the wood with a soft-bristle brush. The detergent removes dirt, and the ammonia neutralizes bacteria. Let the mixture sit on the wood for 5 to 15 minutes.
Rinse teak furniture thoroughly but gently with a hose. Let the furniture air dry.
Apply teak oil to dry, clean teak furniture. Teak oil replenishes teak's natural oils to maintain that wood's smooth, satin-like finish. But be aware that oiled teak wood is more prone to develop mold and mildew, so clean it more often.