In the youth areas the terms are different. A very good friend of mine worked in the youth activities (if that's the right term for the kids clubs) and I think each contract was maybe 12 or 16 weeks, some of the shortest on board.
In the UK (not sure if it's different in the USA) it was fairly straightforward. Applied, face to face interview in London, got the job. She had a degree in Education and quite a few years experience delivering and then managing informal science education along with being a girl guide leader etc.
Looks like you're on the right track with your course, just get a nice relevant holiday job as a playworker to ensure you have lots of the necessary experience. I assume you've already done plenty of that sort of thing already if it's your chosen path though.