Live mussels naturally open and close. People think when mussels are open, that means they are bad. This is not necessarily true. If you spread them out and tap on them, they will start to slowly close. If they are wide open and there is no movement, they are most likely dead.
The best way to store mussels is in the refrigerator. Place them in a colander with ice and a bowl underneath to collect water. Cover the colander with a wet cloth. They will typically be happy in this environment for at least three days from purchase.
Clams open and close as well. The nice thing about clams is that as soon as you touch them, they should snap closed. Store clams in the refrigerator on a cookie sheet or plate covered with a wet cloth. No ice is needed.
To filter out the naturally-occurring grit and sand found in clams, fill a bowl with water and add salt to it until it tastes like ocean water. Drop the clams down into the salty water and leave them for about an hour in the refrigerator. They will filter out the sand and grit into the water.
Oysters are similar to clams in that they will close pretty quickly when touched. Typically, if an oyster is open at all, it is dead. When you tap two living oysters together they should sound like two rocks hitting each other. If they are not open, but they sound hollow when tapped, one or both are dead.
Store oysters in the refrigerator on a cookie sheet or plate covered with a wet cloth. Oysters will last longer than you think as long as you keep them happy.