There are two common practices: a, with water and aeration, b, without water, cool to 3-7 degree and keep in cardboard box.

Ship them without water.  Place the crabs to be shipped in water with aeration.  If they are fresh water crabs add fresh water ice.  If they are salt water crabs, add salt water ice.  The ice must be the same salinity as the water.  Note the water temperature of the water where they normally live.  Bring down the water temperature with ice until they completely stop moving and are stiff.  Do not let them sit in this water for too long or they will die.  Soldier pack them in a "tail-down" position with their arms and legs folded inward toward their bodies.  Their faces should all be looking upwards if they are packed with their tails to the bottom of the box.  Punch a couple of airholes all the way through the box wall with a screwdriver.  Cover them with newspaper or excelsior and place a frozen gel pack on top of the newspaper.  The box should be made of styrofoam and have a cardboard outer.  Make sure that the holes in the sides of the box go all the way through from the outside to the inside of the box.  You can put two layers but make sure you have the layers separated with either newspaper or excelsior (wood fiber from the Aspen tree). Ship immediately.

These can survive outside the water for several hours, the special preparation can help to get good air and other parameters like temperature in optimal conditions.