The big cranes swoop down and pick up the containers, then pull them up and onto the ship. They seem to be able to do this at the rate of about one every 90 seconds, and they never seem to miss the target, or to have to make adjustments to get it just right.
The containers are brought over to the cranes on slightly modified flatbed trucks, one at a time. And there are forklift-like mini cranes that wheel around and load the containers onto trucks.
The truck drivers just drive around in circles all day-- load a container, drive around, unload a container, drive around. The cranes just lift and carry and lift and carry. And the mini-lift gizmos buzz around all over the place.
The whole thing seems incredibly well-synchronized, like this really cool mechanical ballet.