Sadly -- and we see this far more often on Samsung devices than on any other Android manufacturer -- the upgrade will not be available over-the-air (OTA). In order to upgrade their devices, AT&T subscribers must use Samsung's Kies software.
You have to first download Samsung's Kies software, then download the new Android version onto their computers and apply the update to their phones through a sync. If it sounds familiar, it's the same way that iPhones use to be updated (through iTunes).
Annoyingly, Android owners used to make fun of iPhone owners for having to do that. Samsung owners still (often) have to jump through those hoops.
Users can update their Samsung Galaxy S III devices by following the steps provided on AT&T's Jelly Bean upgrade page.
T-Mobile updated its GS3s last month, but used Kies (sigh). Verizon Wireless is still keeping its GS3 owners waiting for Jelly Bean, and it is unclear if it will use the more convenient OTA method, or Kies (we'd bet on Kies).
AT&T has produced a video introducing Jelly Bean. It can be seen, embedded.