Under cold running water, flip the crab over. On its belly, you'll see its apron—it's circular on a female crab and pointed on a male crab. In the picture below, the apron is pointed, so we know it's a male. Use your thumb to flip the apron away from the crab and then break it off, away from the shell.
Stick your thumb into the hole left after removing the apron, and use it for leverage to remove the top shell and carapace from the crab's body and discard it. At this point, crab "butter" and guts may begin to fall from the crab. This is normal. Rinse the crab's body under running water to clean it off.
Remove the crab's gills, otherwise known as the "dead man's fingers". They're rubbery and spongy. Pull them off the crab and discard.
Near the crab's mouth are its mandibles. Crack them off and discard. Rinse the inside of the crab's body thoroughly again under cold tap water. There shouldn't be any more guts, only shell and legs/claws.
Flip the crab around, hold the center of it with both hands and crack it cleanly down the middle like you were opening a book.
Rinse the legs and claws thoroughly under cold running water once more. Pat the legs and claws dry with a paper towel. The crab is now ready to reheat for consumption or to have its meat removed and used in a recipe.