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Place the lobster in front of you, on its belly and facing away from you.
Place a heavy and very sharp knife (a butcher knife is ideal) along the middle of the lobster's body with the tip directly at the head and press the blade down with force (not too fast or you might slip). The Lobster should now be split in 2 halves.
Remove the intestines from the tail (a dark cord running along the middle of the back).
The contents of head and body are not edible, but if you remove the intestines, stomach, liver and gills you can use the remainder and all the shells to make yummy lobster stock.
The tail halves can easily be removed from the shell with a fork.
Remove the 2 big arms with the claws by pulling them out with a twisting motion and break the arms into pieces at the joints.
To open these segments, crack them open with the knife using a short, hacking motion with the blade meeting the shell in the middle of the segment on the front edge. You can now pull the shell open like a cracked egg and pull the meat out with a fork.
Use the same procedure on the big half of the claw. Break off the thumb-like part of the claw and pull the meat out.
The legs are edible as well. You break them into pieces at the joints and either suck them out or pull the meat out with a narrow fork.
If you have no lobster fork, a fondue fork works nicely as a substitute.
A less dangerous method to crack the arms and claws is to use a nutcracker which is very similar to the lobster-tongs you use at classy restaurants.
It is ok to eat the arms, claws and legs using your fingers. However, the tail is to be eaten using fork and knife. At the restaurant, always use the finger bowls to clean your fingers before wiping them on the napkin - lobster gives terrible stains which can not be removed from the tablecloth or napkin. At home it's easier and more convenient to use paper napkins and plastic placemats.