close quickly if you tap on them — if not, don’t buy them. Also, any mussels or clams that haven’t opened after being cooked are spoiled and must be thrown away.
Whether you shop at a dedicated fish store or the fish counter of your local grocery, your best bet is to make friends with the fishmonger and find out the days new shipments come in. Shop then and you will be rewarded for your extra effort with the best-tasting seafood.
At home, keep all seafood very cold — ideally at 32 degrees — right up until you cook it. That means storing it in the fridge on a bed of ice (replace the ice if it melts before you use the seafood). Because seafood is so perishable, use it quickly, preferably within a day of buying it.
More information
FoodSafety.gov has more on all aspects of shopping for seafood and preparing it safely.