Most seafood—if stored in proper conditions—can be held for a couple of days, depending upon the harvest date. This is where it helps to have a good relationship with your seafood dealer, to be sure of the freshness of your fish!
There are several factors that go into the storing of each type of seafood. In general, the best way to keep most seafood is buried in ice with the melt water drained off. If we’re trying to keep fish fresh at home, we typically put the plastic-wrapped (watertight) package in a bowl of ice in the fridge. If we are trying to keep shellfish (such as mussels, clams, oysters, or hard-shell clams) we’ll ring out a wet towel and place it over a bowl containing the shellfish, and put the bowl either in the fridge or packed into a cooler, sitting on a bed of ice. The most important factor is a cold temperature, but it’s also important not to allow the shellfish to sit in fresh water. It also seems to help to allow a bit of airflow around the shellfish, so don’t pack mussels or clams, etc. in airtight plastic.