Whole clams, oysters, and mussels should be alive when you buy them. Their shells should be closed tightly or—as is often the case with steamers and mussels—if gaping, still hard to pry apart. They should smell really good. In this condition, iced or refrigerated and allowed to breathe (never store them in closed plastic bags), they will remain alive and healthy for days. Wash them well before cooking; there may be times you need to scrub clams to remove all the grit.
Shucked mollusks—as scallops almost always are—can be treated in the same way as other fish. Ice or refrigerate them and use them as soon as possible.