If it's brushed finish, I use a green (non-metallic) brillo pad as used for washing up! Depending on how bad the scratches, starting of firm then going lighter and lighter in pressure. The key is moving in dead straight lines. Done this loads of times on bracelets and clasps.
If it's a polished finish you'll probably find Cape Cod polishing cloths come highly recommended, but they only remove the lightest of scratches. Anything deeper, ie that you can feel not just see, is likely to need more professional attention or some kind of mechanical polishing which I haven't ever risked!
Anthony