When you take your purchase home from the fish market, rinse it under cold running water and store it in an airtight container. For the best flavor, nutrition, and texture, keep it in the refrigerator for no longer than two days before cooking it.
As the saying goes, fish, like guests, start to smell bad after three days. That being the case, if any of the fish you're considering at a fish market seem a trifle strong, avoid them. Ideally, the fish in the market will be very fresh, and laid out on ice; if they're rank, something's not kosher.