Barbecue at the beach, in the backyard or on the grill inside. Cook until they sound hollow when tapped.
Microwave - Use a covered dish, cook at full power for 1 minute (or more) per oyster, depending on size. Oysters will open enough for a knife to be inserted to pry shell apart.
Oven - Use a cookie sheet or roasting pan, cook at 450 degrees for 15-20 minutes.
Steam Kettle - Place the oysters on a rack, add a little liquid (beer with garlic or a combination of whole cloves, whole peppercorns, and bay leaves for a real treat), cover and steam for 15-20 minutes. They'll stay moist and tender in the steam.
DON'T OVERCOOK! Oysters in the shell don't always open when they are cooked. Check by tapping on the shell. A hollow sound means they are ready to eat. Always place them flat side up - cup side down to hold in the juices as they cook. However, Pacific oysters are larger than East Coast or all European oysters. These oysters therefore need to be cooked longer, past the "till the edges curl" stage.
Photos on how to shuck an oyster the easy way
Use a stout table knife to open oysters - a pointed, sharp blade isn't necessary. Insert the knife between the shells at the end opposite the hinge (an easier way is to use pliers to break an opening into side of shell near muscle) and, keeping the blade against the top shell, slide the knife toward the hinge. You will cut the muscle from the top shell which then can be pried off. Then slide the knife under the oyster to sever the bottom side of the muscle, and it's ready to eat!