If the sink has a "brushed" type appearance you can use very fine sandpaper (black silicone carbide wet type) and work the area in the same direction as the "existing grain"...some sinks are more polished than others the trick is to match the sand paper grit with the sinks "grit"...shinny sink are just finer grit polished.

On the brushed finished I use a 3M "GREEN" scour pad working with light pressure in the same direction as the finish.