I’ve used this simple method to polish stainless steel for years now. Maybe it’s so simple that it doesn’t need telling. Maybe you already know this trick, BUT just in case you didn’t…
The trick to polishing stainless steel is VINEGAR! If I have a pot I’ve ruined or if my Berkey water filter is covered in fingerprints or if my spoon rest just won’t shine, I wet a cloth with vinegar and wipe it down. Voila! Good as new. :)