What sort of Dispatch do you mean?
There are the Aircraft dispatchers who supervise turnarounds etc or Flight dispatchers who work in the Airlines Operations centre and are involved in Flight planning and control of the aircraft.
Either way though there's only one way in and I'm afraid to say its at the bottom.
You'll need to start off in passenger services before moving to Aircraft dispatch and even then you'll have a fight on your hands as most people want to make that move.
If its Flight dispatch you're interested in then its pretty much the next step as most people in the job have worked on the ramp at some point.
Its a long struggle with a salary thats less than a Government handout but I happen to think its worth it, and for anyone that wants to winge about the job/wages why dont you leave and put us all out of our misery?!
Think about it hard and good luck if you go for it!