I polish stainless steel almost every day on my handmade knives. Polishing is nothing more than reducing the size of scratches in a surface until you reach an acceptable level of reflectance. When I polish steel, I start sanding with a sandpaper grit aggressive enough to remove all surface blemishes. I then progress through grits by sanding at a 45° angle to the previous grit until all previous lines are gone. I usually sand up to 2000 grit and then take my knives to the buffer with a light coloring compound. It's a lot of work but if you take shortcuts you will just have shiny scratches.
Bob