Cleaning Suggestions

Does anyone have some good suggestions for cleaning stainless steel sinks? I happen to be working from home today because my daughter wasn't feeling well and I noticed that my kitchen sink is pretty gross. I think I heard something about using steel wool on it but I would hate to scratch up the sink if I misremembered or something. Oh, and I don't want to use anything that will hurt my animals. Not that they ever get into our kitchen sink but that is where I fill their water bowls and wash all of their food bowls. So it can't be something harmful.