Question about Cranes. The large machines next to skyscrapers, not the birds.?

They can build a column of girders and then hoist themselves atop it. Then once the column is up, they hoist the cross member atop that. Don't forget, there is an engine in the crane. And they can weld things to the girders and all that. So if they need to raise the height of the column they are on top of, they can weld on secure tie points, attach a cable to them and lower the crane with a winch. They don't have to lower it all the way to the ground. Then they can extend the colun by the girders they previously winched up there, which are supported by the column they are on. If this is confusing, try searching for time lapse films of construction. You will see what I am talking about.

There are mobile cranes which can come on site and assemble the tower cranes (these are the very tall ones).

Sorry the only information on Cranes here is of the Feathered variety, you have entered the wrong section sorry.

those cranes assemble themselves. the cab of the crane walks itself up the sections, lifts another section into place and walks up that one until it reaches it needed hight.