To remove water spots, simply dip your sponge in white vinegar and they should rub right off. Rubbing alcohol also works to remove rust if your sink is suffering from a case of the “crusties.”
If stubborn stains seem to be ailing you (thanks to the last tenant), use a mixture of 3 parts cream of tartar to 1 part hydrogen peroxide and buff it over a stain with a cloth. Let the mixture sit and allow to dry before wiping away with a wet cloth or sponge.
From – http://www.apartmenttherapy.com/how-to-make-your-stainless-ste-57954