Combine 3 tablespoons of baking soda and enough water to create a light paste. Apply the paste to a soft cloth.
Rub the stains and oil spots with the cloth in a small, circular motion. Rinse the baking soda mixture thoroughly away. Dry the surface.
Apply your choice of stainless steel cleaner if the spots do not disappear with the baking soda mixture. Follow the product directions to thoroughly clean the surface.
Clean the entire area with a small amount of mild dish detergent and a damp cloth. Rinse the detergent away thoroughly, then use a soft towel to dry the surface completely.