When purchasing live clams, mussels, and oysters, look for:
Refrigerate live clams, mussels, and oysters covered with a moist cloth in an open container for up to 5 days. Do not store live shellfish in water or in airtight bags or containers where they could suffocate and die. Storing live shellfish in salt water shortens their shelf life. Storing them in fresh water kills them. Keep live shellfish alive. Do not cook or eat shellfish that have died during storage.
When purchasing shucked clams, oysters, and scallops look for:
To Store: Refrigerate shucked clams, oysters, and scallops covered in their liquor for up to 5 days, or freeze for up to 3 months.
How to Shuck an Oyster (pdf)