All teams will do private workouts for draft eligible players, including those who have graduated. They can only have four players at a time in their facility, so they will do several days of workouts. Players will fly around the country to see teams they think will draft them.
Workouts include NFL combine like drills with sprints, shuffles, vertical leaps, etc. They also do basketball drills with dribbling, shooting, and some one vs one or two vs two play.
The training and team doctor staff will do extensive physical exams. Team execs and psychologists will interview the players to assess their psycho/social issues.
As the draft nears, teams may fly in individual players to get a final look, or to even toy with other teams to create false interest in hopes of leveraging trades. Players can also leverage the teams by refusing to come to a workout for teams that they don't want to play for, though it's mostly the super elite guys who know they're going to get drafted in the lottery.