Cleaners containing oxalic acid, such as Bar Keeper's Helper in the liquid form, is a good stain remover for stainless steel, notes GE Appliances. A baking soda and water paste can also remove stains on stainless steel.
Use a soft cloth with the oxalic acid cleaner and rub in the direction of the stainless surface's grain line. A soft-bristled brush, such as a toothbrush, can be used if needed, according to GE Appliances. Avoid using the powder form of oxalic acid cleaner because the grit in it can scratch some stainless surfaces.
Other good cleaners include Cerama Bryte Stainless Steel Cleaner and a mild mixture of soap and warm water. Avoid using steel wool because residual particles may adhere and rust.