There are some pretty rigorous qualifications to be drafted to this team. You'll need at least a bachelor's degree, probably in something like computer science, psych, or criminal justice. More important than academic smarts, however, is a sort of intangible, overall intelligence—you need to be able to walk into a room and instantly be able to accurately assess a situation. You need to be able to tell who is jerking you around and who isn't. You need to have an innate feel for power dynamics. Additionally, you need to be exceptionally fit, both of body and mind. You need to be at least bilingual, although having more than just two languages under your belt is preferred. And you need to be a U.S. citizen.
Then, if you meet these conditions, you can file your initial application online, then wait to hear if you've qualified to make the first cut. If they are interested, they'll call you in for an interview, a medical and psychological exam, and a polygraph test. They'll also run an extensive background check on you that will dig up any dirt there may be on you…so don't have any dirt. They will find it. They specialize in finding things. They will interview your neighbors and family members (plus potentially any of your Facebook friends), look at your phone records, look at your online viewing history (yes, they can see every site you've been to), and hack into your email accounts, etc.
They are not just doing this to make you feel violated. They are doing this to protect our country, so that some undesirable doesn't slip through the cracks—you have to be willing to give up most of your personal rights if you decide to sign on. It's just part of the job.