EVE Uni’s wiki is often the first and best stop for things like this, specifically this page in your case: Applying to EVE University - EVE University Wiki
You have to authorize the character you want to apply to the Uni with on our EVE Uni Alliance Auth. Just follow the steps one by one on the wiki and you should be good.
You can also just join our Discord (and Mumble) as a guest though a lot of the steps like registering on Alliance Auth are the same: Connecting to EVE University Services as a Guest - EVE University Wiki
If you need help with your application you can also reach out in-game to our Intake & Progression officers vie EVEMail: Intake & Progression Department - EVE University Wiki
Hope that helps!