The horizontal part of the crane (the top of the 'T') is assembled on the ground first then jacked up for the first section of the tower to be inserted. The assembly is continually jacked up allowing more and more sections to be slotted in until the required height is reached.
Some towerblocks are built in a similar way with the roof first being assembled at ground level then jacked up for floors to be built below. These are known in the UK as "jack blocks" but I'm not sure whether this is an official term or an international one for that matter.
Alasdair Bailey