To get to the Georgia Dome, you’ll want to exit at the W1 Dome/GWCC/Phillips Arena stop OR the W2 Vine City. The Vine City stop will have less traffic and put you more easily on street level without all the underground climbing at the W1 stop.
If you are coming from the north or south lines, you will have to transfer at Five Points. This is where it can get tricky. Make sure you follow signs to the WESTBOUND platform. Many times I have seen people go up a stairway or escalator that is to the eastbound platform, and there is no way to get to the train you need that way. Generally, it is usually better to exit to the outside (not center) platform. When in doubt, just follow the signs as there are plenty that can direct you to the westbound train.
Once you get to W1, merely follow the signs pointing to the Georgia Dome (which has its own exit separate from Philips Arena). Or if you get off at W2, Vine City, merely walk down Rhodes Street when you exit the station (see map). You can’t miss seeing the Dome.