I'd suspect you would be asked to take a picture of your vaccination card and show it at one point or another in the fall. Most schools are now offering monetary rewards to students to get vaccinated. Purdue (where my oldest goes) is going to offer $10,000 scholarships to 10 different students (chosen randomly) over the summer who have been vaccinated. Baylor (where my youngest is going to go) hasn't mentioned any similar program yet, but both schools have made it clear that if you're not vaccinated, you'll be undergoing weekly covid tests in the fall.

You can pretty much assume any school that isn't forcing its students to be vaccinated will be requiring the non-vaccinated to undergo weekly covid testing.