It’s easier than it sounds.
“Oysters on the half shell” sounds fancy, but if you can pry open the shells, you’re almost there. Grab an oyster knife (like the Dexter Russell stainless-steel oyster knife, $20) and a dish towel and follow these steps.
Clean oysters vigorously under cold water with a scrub brush. Grasp an oyster in the towel, with the flat-side up and the hinge (where the shells meet) exposed. Poke the knife into the hinge. Twist the knife back and forth—like turning a key in a lock—until the top (flat) shell pops open.
Slip the blade along the inside of the top shell, severing the muscle (the oyster will rest in the bottom shell) and being careful not to spill the liquid. Discard the top shell.