All major airlines fly to Atlanta. From there, a shuttle service, Groome Transportation (855) 360-0010, can provide the 90 minute trip to Athens for $37 one way. You should contact them directly to make a reservation. Groome Transportation drops off and picks up at local hotels and near the math department, at the Georgia Center.
If you are renting a car at the Atlanta airport, here's the best route to the center of town.
There are a couple of other ways to get to Athens. Sometimes you'll find cheaper rates if you fly into Greenville-Spartanburg Airport (Airline code GSP). It is a 2 hour, low traffic drive to or from Athens. You will need to rent a car if you land there.