Live crab (fresh meat) should not be stored in the fridge. They must be kept alive (typically in aerated water) until they are cleaned and cooked. Putting a crab in the fridge will kill them and you should never cook a dead crab. Cooked crab meat, if stored in an airtight container, can last three to five days refrigerated.
Freezing cooked crab meat is quite easy. Simply store it in an airtight container or heavy-duty freezer bag. You can also wrap the meat tightly with foil or freezer wrap. Frozen crab meat will maintain its best quality for up to three months.
Placing crab meat in the refrigerator is the safest and most effective way to thaw it. Because frozen crab is prone to dryness, be sure to substitute its loss of natural juices with a wet ingredient like mayonnaise.
Cinco de Mayo
Pick up the crab with your hands, place a thumb in the hole where the apron was (you may need to pry it open with a butter knife), and pull in one motion to remove the top shell (the carapace) from the rest of the body. Discard the carapace.
Using a butter knife, cut the front (mouth) of the crab off and scrape away any remaining bits of gill and viscera (often called “mustard”) left on the body of the crab. 
Starting at the back fin of the crab, pull the delicate bits of shell away and pick out the meat inside the body. Carefully pull the legs away from the body and pick out any meat attached to the leg joints. Twist the legs to crack open the shell and pick the meat out. Pick the shell from each chamber in the body of the crab and pull out the crabmeat.
Using a seafood mallet or the handle of the butter knife, firmly tap the shell of each piece until it breaks apart. (Don’t hit the shell too hard or it will splinter into the crabmeat.) 
Wiggle the pincer and gently pull it away from the claw. 
Serve with melted butter for dipping.