On Discover University -- I've been learning a few things by making mistakes.
First, I forgot that you had to wait a couple of days to get accepted. So, hint#1, apply at the end of your Well-Educated Sim's first week. They'll have some skills then.
Then, enroll the Saturday before your Sim's turn comes up. That is, if your Well-Educated Sim is the third Sim in your rotation, switch to them on the Saturday of the second Sim. (I hope that makes sense.)
Do not switch to the rest of your household while your Sim is in class. This kicks her out of the class with a hit to her grade.
To complete the Academic aspiration, your Sim needs to attend 3 guest lectures. These take place between 5 and 7 pm. I'd advise a light course load for the first week to get these out of the way, especially if your Sim has a toddler.