Check out your Congressman's web page. When the application process is open and deadlines will be posted there. You will likely begin the application and gathering recommendations, etc the summer before your senior year. Each MOC has a code with SAT and ACT to have test scores sent directly to them, just like colleges. Each MOC has a different process and requires application submitted a certain way. Be sure to follow each.......to the letter.
MOC's change all the time.........their staff must pass along the apps in progress to the new one, or finish the process before the newly elected MOC would take office. You cannot worry about this. You have no control over that, so no sense in worrying about it.