There is a subway, called Marta, but most people drive. If there is more than one passenger in a car, take the HOV lane, which goes faster and smoother than any of the others. And be ready for lots of slow downs. You do not hail cabs in Atlanta.
Parking and car rental at the airport is tough, so if you can take the Marta into the city, do it. If luggage is light and time is not an issue—it should take an hour to reach the Lindberg station in Buckhead—try the path with the fewest headaches. The major thoroughfares are I-75 and I-85, with a perimeter road of I-285. The natives know the back roads, but they are choked with traffic too, so be patient and stick to the easiest route.