What I would do is.... write to all places that you would like to be employed at (no point writing to the other end of the country if you aren't prepared to move there), and ask if there are any current vacancies, and if not, when there might be any.
Every few months write again (don't know how long this might take!).
You yourself must know why you're interested in the job- you say that you have a non-aviation background, well now is the time to get a bit more genned-up. Visit ATC units, study aircraft books- know a 747 from a Cessna- heights, speeds etc.
Just ask yourself what you would ask if you were doing an interview, and things should become clearer.
Good Luck.
