Pull the legs (and the head if it's attached) off.
Gently peel the shell off. If you would l like to leave the tails on gently remove the shell up until the last segment of the shell.
To remove the vein, use a small pairing knife to cut a small slit in the back of the shrimp. About 1/4 inch through. Use the knife to gently remove the vein and discard.
Keep the shrimp cold in ice water until ready to use. Pat dry before using.