Qualifications
The qualifications for becoming a fighter pilot are deceptive. On the one hand, it's ridiculously easy to join our nation's armed forces. Except under special circumstances, if you're an American citizen at least eighteen years of age or older (seventeen with parental consent) but under thirty-five, can pass a physical exam, and you've earned your high school diploma or GED, you can join the service.
That's just the basics though. To actually become a pilot you also need to be an officer, but those qualifications are only slightly more critical: being at least nineteen but under thirty-six and having earned a four-year BS or BA degree are the main differences (source).
From there, things get a bit more...classified. Both the Navy and the Air Force have traditionally been fairly secretive about what exactly the "right stuff" consists of. There are several different training schools where one can learn to be an effective fighter pilot (with one literally called TOPGUN, no lie), but the qualifications for admittance seem to be a matter of national security.
What we do know is that if you want to be a fighter pilot you have to be smart enough to handle all the controls, determined enough to handle all the tests and training, and physically fit enough to handle all the g-forces (not to mention all the stairs you'll have to climb to get into your cockpit).
You should also be able to take orders like a computer, handle pressure like a brain surgeon, and have a level of emotional and mental maturity that would stun Sigmund Freud into silence.