You'll essentially have two options - you can park right around the stadium. There's a few "official" parking lots around the GA Dome/GWCC and plenty of..... not official ones

Expect parking to be roughly $20, give or take a bit. You can also drive to a MARTA station that has parking (there are a few that don't) and it has free same day parking, and train rides are $2.50 each way. GA Dome/Vine City are on the East-West MARTA line. If you choose the MARTA route - I cannot stress enough how much happier you will be if you walk across the street after the game to the Vine City station as opposed to boarding at the GA Dome station. You'll be able to board and maybe even get a seat before the train gets to the rest of the herd.
If it were me - I would park somewhere else and take MARTA or Uber to the game. I'd give yourself a good 45 minutes from getting off either of those to get in, get to your seats and concessions, perhaps another 30-45 minutes if you drive and need to find a place to park.