To prepare live scallops in their shells, steam, sauté, or bake them until they open completely and pull away from the sides of their shells.
Perhaps the easiest way to cook scallops in their shells is to sauté some garlic and herbs in butter, add some white wine and bring it to a simmer, then add the scallops and cover to steam them.
If you would rather cook them on the half shell (for stuffed scallops, coquilles St. Jacques, etc), steam them just until they open, prepare the meat according to your recipe, and then continue to cook the rest of the way (usually either baking or broiling them).
Scallops can also be “cooked” with acidic ingredients for ceviche.
Ingredients commonly paired with scallops include citrus fruit, cream, tropical fruit (especially mango), thyme, butter, cilantro, garlic, shrimp, bacon, black pepper, parsley, vinegar, tomato, white wine, wild mushrooms & peppers.
Take care not to overcook scallops, as they will tighten and become rubbery.