(Directions for right-handed; reverse for left-handed)
If the heads are attached, twist them off to remove. Hold the shrimp in your left hand, tail pointing away from you, back of shrimp facing to the right.
Hold the deveiner in the right hand, tip and serrations pointing down. Insert the blade into the top portion of the shrimp and slice toward the tail along the contour of the shrimp, lifting blade off the shrimp as it goes. The sharp edge splits the shell as the serrated teeth grab the vein. Pull off the shell at the point it joins the tail with your left hand while holding the shrimp between thumb and forefinger.
If you prefer to leave the tails on: Do not go all the way to the tail with the knife blade; stop at about ¼" from the end of the shrimp body where the last two shell sections meet. Pull off the shell at this point.
If you want to butterfly the shrimp: Complete the steps above, leaving the tails on. Reverse the deveiner in hand so tip of blade and serrations are facing up. Slit back of shrimp from tail to head, about 2/3 through.