What training is required to become an air traffic controller?
Training for US path is(I'll take this information, post hiring, since they keep changing how they hire, and assign facilities, also length of times are approximate and might vary):

FAA Academy(Oklahoma City, OK):


~6 week AT Basics Course(If you went to a CTI(College Training Initiative) school, this course is skipped)
Then if you're split depending on which area you're going to, Enroute, Tower, or TRACON.
Tower course is ~8 weeks,  TRACON course is 1 month (or 2 if you're going to a bigger facility and they put you in a supplemental course), and Enroute, I'm not positive is around 10 weeks or so.


Then you move to your facility. At your facility, your first days you'll spend learning various materials, and then be given classroom training, including Computer based instruction, an actual instructor time(if the facility is large enough), and also lots of study time to memorize all the maps, and various items you will be tested on. Then, if your facility has the ability, you'll do some simulator problems. Note: you might only get the classroom and simulator for only a subset of positions at the facility, depending on how they break up the training.

Then after all that, you head out to the operation, and will usually start training on some subset of positions that are at the facility. You'll receive training on each position, until you've demonstrated that you're competent to work it on your own. Once/if you get to that point, you're given a certification check by your supervisor, and if you pass you're certified to work that position. And you repeat that process for each position, and possibly having to return to classrooms/simulators for any additional positions, and repeating the process again. Once you've finished all the positions you need you're a fully certified controller at that facility.

Each time you move to a new facility, you will have to repeat the classroom and simulator, and on the job training at the positions at that new facility.

There's far more detail and nuance than I can easily explain here, but this is a general overview of the process.