Pick up MARTA down by baggage claim. It's very clearly marked.
MARTA will be $2 for a silver card, $2.50 per trip or they let you buy multiple day trips which let you get on/off multiple times in one day.
Atlanta has a very active transit system so Google Maps is a great tool to figure out what MARTA line to take and what stop to get off at. Just enter in a search for your destination, ask for directions, then click on the mass transit icon in Google Maps and it will tell you exactly what train, direction and stop.
The only thing I found dicey was very early morning flights out of Atlanta so double check what time your first MARTA arrives AT the airport if you are going to take the train on your way back. I've never missed a flight but better safe.