When the building work begins the first tower crane is built by a mobile crane that arrives on site, builds the tower and then leaves. Then, as the tower needs to get higher it jacks itself up as it goes along. The jib, control room, counter balance etc, are all there from the initial build. The first tower crane can then build any further tower cranes that are needed on site but only within it's reach. Any out of reach will require another mobile to do it.
Sections of a tower crane weigh very little but some of the largest mobile cranes in the world are needed to erect them as the weight it is able to lift is directly proportional to the distance from the lift. For example a crane capable of lifting 100 tons if the lift is directly below the crane might only be able to lift say 2 tonnes if the lift was 30-40 meters away from the base of the crane. As modern day developements are often in inner city areas access and therefore proximity to the lift are often a problem.
We recently moved a 250 tonne crane into Central London but it stood for weeks waiting for permission from the Underground to lift and erect a tower crane as it was deemed dangerous to exert such enormous ground pressures without adequate foundations. The nearest the mobile could get was 50 metres from the desired point of lift and so a 250 tonne crane was needed to make a maximum lift of 1.5 tonnes or thereabouts.