How can I tell if fish is spoiled?

Fish should smell fresh and mild, not fishy, sour, or ammonia-like. Whole fish and fillets should have firm, shiny flesh and bright red gills free from slime. Dull flesh may mean the fish is old. The flesh should spring back when pressed and should not appear dry or mushy in any areas.
 
Fish fillets should not display darkening or drying around the edges. Nor should they display green or yellowish discoloration.
 
Source(s):
FDA "Fresh and Frozen Seafood -- Selecting and Serving it Safely"