From what I have read:
The crane "grows" using a jib, hydraulics, and sections. When the building is completed, the arms are dissassembled on the roof (they may be removed by another crane attached to a truck, or by other equipment on the roof?), and the process is then reversed (each section removed floor by floor by equipment inside the building). The jib is lowered as each section is removed, until there is nothing left, and the jib assembly is removed at ground level.
I may need correction on this one though