The easiest and probably most cost effective thing to do would be, look in your local yellow pages under Appliance, Bathtub, or Tile Refinisher's. It shouldn't cost you any more then 30 - 40% of what it would cost to replace the sink, if you use a professional.
If you want to DIY, then do a web search using key words like "refinishing kits".
Notwwrothy is the fact that, due to the abuse kitchen sinks endure, they probably have the lowest life expectancy of any household item that can be refinished.