Mussels are very versatile and can be steamed, broiled, deep fried, even grilled. But generally, they are steamed first, even if they are to be finished by some other cooking method. Steaming them causes the mussels to open so you can get them out of their shells, either to eat, add to a salad, or toss on the grill.
Another reason mussels are steamed is that they release a flavorful broth as they are cooked, which you really don’t want to dilute and lose in a gallon or more of boiling water. Mussels can be steamed in just about any liquid, but white wine or water are probably most common. In simple preparations, the cooking liquid is often just poured over the finished mussels as a sauce, or it can be transformed with other ingredients into something very fancy.
To steam mussels, bring a cup or two of water or white wine to a boil in a large pot or steamer, add the mussels, and cover. When the steam begins forcing its way out from beneath the lid, lower the heat to medium and steam for five minutes. If you can do it carefully with pot holders or a kitchen towel, shake the pot to redistribute the mussels, and cook for another three minutes. Check to see if all the mussels have opened. If not, cover the pot and cook for another two to three minutes. Discard any mussels that do not open. If you are going to fry, broil, or grill the mussels, remove them from the pot as soon as the shells open, and then cook them briefly with the second method, to avoid overcooking them.
After you remove the mussels from the pot, you can serve the sauce as is, reduce the cooking liquid to make it thicker, or add spices, herbs, aromatic vegetables, or other flavorings (fish sauce, soy sauce, tomatoes, etc.), make it richer with cream, butter, or mayonnaise, and/or thicken it with a roux or cornstarch. The mussels can be served in half of the shell or removed from the shell.