1. Press the [Esc] key to open the menu while in game
   
2. Click the "Controls" tab
   
3. Click the "Keybindings" tab
   
4. Observe the controls under the "Crane" section

Note: Fast move only applies to the crane arm and tower rotation. It does not affect the lift or cable movements for physics reasons.

In order to operate the crane you must enter the cabin and assume the controls by interacting with them either with E or interaction-mode. From there following the controls you should be able to fully operate the crane either from a dock or on a boat.

The travel lift is for moving large shipping containers. It also has space on top for Nautikins to ride or stand.
The hook lift is for moving small shipping crates.
The magnet lift is used for lifting vessels out of the water. It is useful for putting smaller boats on larger boats. You will not be able to pick up vessels that weigh far more than the vessel that has the crane. Dock cranes that are not attached to boats do not have restrictions. In all cases the magnet should be used with caution.

The base of the crane comes with a nice ladder to help you climb to the other areas. It is either mounted to a dock (part of the map) or can be mounted to a boat as an available part.

The second level of the crane offers access to the cabin and the crane arm should you desire to climb it.
The 3rd level of the crane offers an observation platform as well as a nice crows nest feel.

The crane offers 3 perspectives

Functionally speaking, all the views are the same, its really a matter of preference. I like the lift view.

Cranes also have built-in lights, similar to vessel lights they can be turned on/off with L (or other keybinding).