Baking soda is fantastic for cleaning stainless steel. I have recently allowed my sink to get into a terrible state - oh the shame! But take a look at the effects of five minutes with some baking soda and a damp cloth.
It really is blindingly simple. Scatter some baking soda over the sink, scrub with a damp cloth and then rinse. Buff dry with a rag or tea towel for extra shine. So what are you waiting for? Go make your sink shiny!