easiest way to remove scratches from stainless steel?

Find which way the grain runs first and only ever rub along it, never in circles. For fine scratches a paste cleaner like Bar Keepers Friend on a damp cloth, then rinse and dry. Deeper ones need a scratch kit with graded abrasive pads, but go gently - it's easy to end up with a shiny patch that looks worse than the scratch did. Check it's not a coated fingerprint-resistant finish before you start. Anything abrasive will strip that coating.