The background check begins when you begin the pre-employment process... you have completed CTI school, taken AT-SAT, and begin the FAA paperwork process. From what I understand it's pretty extensive, back when I was hired they even dug up an old open container summons I got at a Metallica concert
(let the jokes fly fellas...)
My advice when dealing with the Gov't is to be honest, don't hide anything. If you're honest up front, they very well may hire you, I have seen many people hired with marks on their records, but if you lie and get caught you will be terminated and there is nothing you can do about it.