How should shellfish be cooked?

Shellfish should be cooked to an internal temperature of 145°F. Steam mussels, clams or oysters in the shell for 5-10 minutes after the water begins to boil.
 
Submerge lobsters head first into a pot of rapidly boiling water. Start timing when the water returns to a boil and cook 10-12 minutes for the first pound and four minutes for each additional pound. Lobsters will continue to cook when removed from boiling water, so you can take them from the water just before they are done or drop them into iced water to stop further cooking.
 
The same goes for shrimp. In general, boiled jumbo shrimp take about 7-8 minutes to cook, large shrimp 5-7 minutes, and medium size about 3-4 minutes.
 
Scallops cook extremely quickly. Heat a pan, season the scallops lightly, and sear them in just a little oil or butter for only 30 seconds on each side. 
 
Raw crab can be steamed, fried, or boiled. Cooking times vary.
 
Source(s):
Nova Scotia Agriculture--Food Protection and Enforcement Division "Shellfish Food Safety"
Whatscookingamerica.net "All About Shrimp"
Shellfish-lovers.com "How to Prepare Scallops"
Howstuffworks.com "Cooking Crab"