There are a few types. Some more modern cranes jack themselves up and then back down after wards. There is a large mis-conception about tower cranes. Many people think they can handle larger loads than portable jib cranes. This is not the case. The advantage of a tower crane is its cost and ability to see. The ones that are not capable of jacking themselves up are erected and taken down by large jib cranes with many times the lifting capacity and cost.
they are put up section by section with another crane