Transportation is available on campus, but not really necessary. Most students get around campus just fine and rarely rely on taxis or buses to get anywhere (thankfully, the bars are so close to housing that there's little drunk driving). Walking is the best way to get around campus, and students really only use their cars for groceries, quick errands, and so on. The campus is not very big, and even for students who live off campus, you are never that far from where you need to go. But, if transportation is needed, it's available, which can be nice, especially the bus to and from Columbus. While it may not be needed to get around campus, public transportation is available and convenient.
Getting outside of the city can require a little more planning. It's not impossible, but you'll have to call some service, most likely. Make sure to book reservations early and check online for full listings of all transportation services in and out of Athens.