brilliant question! though we've never fully discussed it, there are tons of throwaway comments made by cryonn that we can use to deduce what the enrollment is like!
For example, there are mentions of tests across a few character posts, and the phrase 'accepted at Karma high' is bandied about a bit- meaning that, of course, it's very selective. Though not so selective that only the upper echelon can get in- Cinaed and nera (both whom come from low income families) are able to get in. And people with powers that do not fit well for herowork in the state they are in also got accepted (sorry, Gwen and Pamela- you need to train harder or unlock some extra dlc because you're getting bodied by most of your classmates (though i admit Pamela is the worse of the two; the soap has battlefield utility, but Pamela's electricity is very weak)). So i assume the school isn't actually a hero school at all- that is, it seems that while it might be the focus of the story, it is not the focus of the school itself. Or maybe cryonn doesn't think about these things before he accepts a character- but i digress.
I assume the enrollment features some sort of test, payment, and maybe an interview? I think that was mentioned once. i think that's a safe assumption