Over time, stainless steel cooking items tend to build up a film that it often seems no amount of scrubbing can remove.
The quickest way to remove burnt on stains or scorches is using a metal polish or cleaner, the type you'll find at your local grocery or hardware store. But there are other options for cleaning stainless steel pans you can try at home first.
Wear gloves to protect your hands from the metal polish and the metal from fingerprints when cleaning stainless steel pans.
Cotton is best, but rubber works as long as you wash a new pair first. (Any sulfur that remains on the gloves could tarnish the silver.)