How do cranes get to the top of skyscrapers?

Slate has an answer to the question you've been pondering:

[T]here are actually three ways: 1) the external climbing method, in which the crane—the arm plus its tower—expands upward along the outside of the building, 2) the internal climbing method, in which the crane builds a few floors at a time from the inside and then “jumps” to a higher spot, and 3) the “skycrane” method of airlifting in a crane on a helicopter. (Engineers at 1 WTC are using both of the first two methods.)

Steve Clowney