Tower cranes are cranes which are set up next to buildings and are really lofty (according to the height of the building - a bit higher). They are used to lift heavy objects up and bring heavy objects down at any height in the limited distance the tower crane has been set. The distance that is being talked about is the vertical difference.
step 1 :Get your dogman license (a dogman is the person that slings up the load and directs the tower crane)
step 2 : Know your stuff! Memorise the material you get about dogging and tower cranes, read up and know strengths of materials and the weights of different materials, if you want to be a tower crane operator you should be able to look at lifts on a construction site and be able to know what items weights are to within a 15% variance.
Step 3 : Get a start with a mobile crane company, it is unlikely you will get a start on a building site with a tower crane with no experience as these cranes can often not see the dogman, it is a very skilled dogman that directs the crane and understands how it moves. As a beginner you will probably be assigned as a fill in dogman, getting as little as 2 week. Yet you are expected to 'stay loyal' and not run off to another company, stick at it and as you get better you will get more work.
Step 4: After a year or two you should have enough experience to move onto the tower cranes, make sure you make contacts whilst working, often you go to building sites of builders that use tower cranes, you could always have a discreet chat to the foreman or project manager if they have the time and you get on well with them. If they see you have a good attitude and can do your job well you are halfway there.
Step 5 : Get your tower crane license. It's a workcover license like the dogman license you got. It only takes a week.
Step 6 : Now you are on a site working with tower cranes remember even if you are not operating you are learning how they move so you are on your way. Talk to the operator about wanting to be a tower crane operator, if you get along and the site is not to busy you might be able to do a few hours here and there doing easy lifts. Be respectful of the builder and the site by asking them if it is okay if you operate the crane here and there, highlight the benefits of having another tower crane operator on site (mostly being able to operate the crane in case the other operator is sick, cannot stay back etc).
Step 7 : Get other qualifications that are relevant such as your riggers license, at times you won't have tower crane work so have something to fill in the gaps till you are back operating the crane.

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