Bar Keepers friend and a soft damp cloth.
Ever get blood on stainless steel? The above works every time...
The active ingredient is Oxalic Acid and works well to breakdown iron oxide deposits on metal. For light stains the Bar Keepers friend should work. When I need to be more aggressive, I buy Oxalic acid in powder form at Ace Hardware. I mix this with water. The solution is used to remove rust from motorcycle parts - inside fuel tanks, bolts, levers, etc. This works on chrome plated parts and on stainless. It does not affect the parent metal.
I have also used phosphoric acid on metals very successfully. You can buy that at the hardware store. It is usually called concrete etch or TSP.
Sometimes the stain can be below the metal surface and sanding will be required as described by elpenguin. Try the Bar Keepers friend first.