I’m using the word “trip” specifically.
The Simple Answer
A trip is your getting from point A to point B, and your fare is to get you to that point B. You pay once even though you may use several buses or trains to get there. You’ll have to pay again when you go back to point A, though. There is no way to have a single fare get you out and back.
The More Complicated Answer
To get from the Carter Center to the Georgia Aquarium, for example, you could take the 102 bus to North Avenue Station, then the Red/Gold Line train to Peachtree Center Station. This is two legs but one trip, so you only have to pay once. This is handled via a transfer.
When you get on the bus, you’ll pay $2.50 and get a transfer to the train. If you’re using a Breeze Card, the transfer is done automatically. If you paid in cash, you’ll have to ask the bus driver for a transfer when you pay.
Transferring between trains isn’t really a transfer like between buses, but it still doesn’t cost any more. As long as you don’t leave the gates, you’re still using that one fare. I’ve gotten on the Red Line at North Springs, got a Gold train at Lindbergh, ridden it to Doraville, then rode it back south to Chamblee all on one fare. As long as it hasn’t been four hours (I think), there shouldn’t be an issue.
Transfers don’t work to or from the Atlanta Streetcar. You still have to pay $1 to ride and also have to pay for your connecting bus or train.
The Details
Transfers do have a limit on the number of legs and duration of your trip. With a standard fare, you get four transfers in three hours, so you will probably never get close unless something really out of the ordinary is going on. I can imagine this might come into play if the trains stopped running for some reason, but I wouldn’t even worry about hitting the limit if you’re just going from point A to point B.
There is a very loose definition of “direction” when transfers are involved, so try to avoid zig-zagging across the city. If you take the 102 bus west toward North Avenue Station then get on the 2 bus headed back east, the system might think your trip is over and charge you another fare for the return. I have seen bus riders get denied and the operator tell them it was because they were going in different directions.