I don't anymore but I used to. Here's how they do it here:
You apply, get hired, background-fingerprinting-etc. (Took me about a month before I was actually able to work.)
Once you're "on the list" they call you. A LOT. Our phone would ring every few minutes from 5-10 pm and from 6-8 the next morning unless we punched in the code for "stop calling us today." If you are already reserved for a job, they don't call. Most calls are for the same day (am calls) or the next (pm calls) but occasionally they come up ahead of time.
We also have a website, so the last year I told it not to call me AT ALL (it gets to be SO annoying!) and just signed myself up for assignments through that.
I was able to work as much as I wanted. Every day, there's always a need. Or less if I felt like it.
It can be easier if you get on well with a school you like. They can give you their "good jobs" before they go to the list, and it helps if you know some of the people. There are schools here that I won't take a job from, even if it's the only 1 available. And there is 1 school that I would actually cancel other jobs to go there and help them out.
If you are deemed qualified, the cushiest job (except for the schedule) is a long-term placement. You have the same class every day for weeks, and actually have to teach them instead of just babysitting. Before I got pregnant, that was my specialty.
I have to warm you: after teaching fulltime, telemarketing, waiting tables, fast food, tow dispatching... subbing is the most stressful job I've seen. I was doing it to be "in the system" if a fulltime position opened up, w/o that option I wouldn't have. It depends on the school & the kids, but don't assume it's an easy job!
Oh yeah -- districts are different but most of them have pretty thorough websites. They hope it will stop people calling them constantly with questions. Check out that for yours, it will probably tell you more than you want to know about rules, pay, etc.