Many people who don’t have stainless steel think that it never gets stained. Many people who do have stainless steel, do not realize that it requires special cleaning.
General cleaning should include warm water and a soft cloth. You do not want to scratch the stainless steel. You can purchase special polishers to improve the finish of the stainless steel if it gets scratched, but I don’t know how well these work.
To remove rust stains, I cleaned the stainless steel with vinegar and a lot of rubbing. I used the scratchy side of an old sponge which scratched the surface of my garbage can, but it’s a garbage can and I don’t mind so much. The above photo shows the worst section partially cleaned, and this photo here shows how clean it got from about 20 minutes of rubbing. I could work on it some more, but I won’t. My bf can if it’s important to him when he gets home. This should work great on sinks, but be careful with stainless steel appliances that you don’t want to damage the finish.
I got the suggestion from Apartment Therapy, but now thinking back to girl scouts as a kid, we soaked pennies in vinegar to clean the rust off them. Smelly but effective. And it’s great to avoid using harsh chemicals that can have a major impact on the environment.