It doesn't exactly clean the stainless steel - you should still wipe it down with a soapy cloth to get it clean. But baby oil takes out any small scratches and blotches. Just a few drops on a soft cloth (bit of old t-shirt ideal) and you'll see the effect straight away.
Theres only one thing for stainless steel and thats an E-cloth, use with very hot water and nothing else ( you need to wear two pairs of rubber gloves so you can use really hot water) The E-cloth will remove all dirt and grease. Don't think that any old microfibre cloth will do it must be an E-cloth.