Basically, after winter break, the office sends out an email about Team Leader positions for next year, and they will try to sell it to you as a great opportunity. A bunch of people will apply, most because they are afraid they won't get a job offer after CY ends.
In February, you apply online. Standard application (with 5 CY specific short answers) and resume with two letters of recommendation. One has to come from your PM (your TL cannot recommend you) and the other your classroom teacher usually.
Basically everyone gets an interview. They scheduled it on a work day, and when I walked into the interview, one of my team members had just left, so secrecy of who is applying is not really possible.
They get back to you really fast. I was rejected and put on the wait list. Many people have received grad school opportunities or other job acceptances by then, so if you are put on the wait list, don't sweat. You might just might get a chance to serve.