Eating crawfish quickly takes a little bit of practice, just like eating lobster. The general idea is to twist off the tail, and pull, squeeze or suck out the meat it contains. There are three things which makes this task easier. One is to cook the crawfish just long enough, the others will be discussed below. Always check to make sure your crawfish was in fact alive when cooked. Some not-so-lively ones always slip through the cracks. The tail should be curled and relatively stiff. As long as you pay a little attention to this possibility, your should figure out "which one of these things does not belong here."

STEP 1:  Take a sip of the beverage of your choice and talk about how big this one is.  Twist and separate the tail from the rest of the crawfish. Bending the tail sideways works better than up-and-down. The head may be discarded.  Some enthusiast enjoy tasting the spices in the body and "suck the head."
STEP 2:  Peel off the narrow bands of shell material at the opening to facilitate removal of the meat (a couple sections). Holding tail, gently pinch it along its length to loosen the meat. (Just like squeezing oranges helps the skin come off better).  You may now dunk your crawfish into the sauce of your choice.
STEP 3:  With a firm grasp at the base of the tail, pull the meat from its shell. If you do it right, it will come out quickly and intact. The crawfish is completely cooked-the vein may be removed for aesthetic purposes, but it is not necessary.  Another option:  Gently push the meat out with your forefinger and the FLAT/BOTTOM part of your thumb while pulling or sucking on the body end of the tail.  Take a sip of the beverage of your choice or grab another crawfish. Talk about how easy that one was.

 

Taken from a crayfish wholesaler at http://www.communique.net/~lacraw/directions.htm
Here are some recipes for crayfish boil.  (Recipes here!)