Doing research for my book, SNACKS: Adventures in Food, Aisle by Aisle, I asked Chef Clark the best way to store seafood at home. His answer started out simply, "Just like it is displayed at the market, on ice," but then it got slightly more complex, and interesting:
For every 2 degrees above 32 degrees that you store your fish for one day, it loses one day of shelf life.
Most home refrigerators hover around 40 degrees. So if you bought tilapia on Tuesday, flopped it in the fridge, and didn't eat it until Wednesday's dinner, the fish instantly aged four days. However, if you store your fish between the freezing point of water, 32 degrees, and the freezing point of fish, 28 degrees, your fish will remain true to its age.
When you get home, place your fish in a plastic bag, but please, never seal it. Sealing traps gasses and encourages the fishy order. Set the bag on a plate or shallow bowl of ice (be sure the bag is folded away from the ice so melt won't get in) and place a light amount on top of the fish. Store it in the coldest part of the refrigerator.