from How to Cook Italian, by Giuliano Hazan

1.  Pry open the shell from the belly of the shrimp, working your way to the tail.

2.  Snap the center part of the tail back then gently pull the shell off by grabbing the very tip of the tail.  You should end up with the flesh from the tail still attached to the shrimp.

3.  Use a pairing knife to make an incision along the back of the shrimp and pull out the black vein if there is one.

4. When deveining cooked shrimp the vein may not come out as easily as when they are raw so wiping it off with a paper towel may help.  Do not worry if some traces remain.