Jane, it goes in three parts usually.
Initial screening include a battery of tests (ASTB), demonstrated physical exam criterion met, and various interviews. You typically need to also have demonstrated the ability to acquire a university degree with better than average marks.
Then, there is initial flight training. This isn't just training, it is also a screening process. Some things you don't find out until people try to do them. Air sense doesn't penetrate all skulls.
Finally, there is the minimum performance standard. If the first two criterion are met, one must still acquire sufficient flying and decision making skills in a finite period of instruction, or the USN or USAF will not keep investing time and money into the prospective aviator.
You've asked a fairly big question.
What is it you really want to know, Jane?
I can tell you with certainty that presently, that is how it works, in the United States Navy.
Ten years ago, the screening tests were deemed to be less than suitable, and a five year program/overhaul was initiated. This was in part due to a number of the tests being compromised, and in part due to the medical, psych and learning/education experts believing that better screening tools could be applied.
Twenty years ago, mostly the same, but simulation fidelity to actual flying wasn't all that great.
Thirty years ago, once again, the same, thgough there began to be screening quotas cropping up for selected demographics to overcome systemic bias (or the perception thereof). One still had to show that one had the skills to fly, however, to get through it.
Roughly forty years ago, you typically had to have a penis to get assigned to flight training ... but that was in the process of being changed.