To join a GC, you need to progress in the main story until after you beat Ifrit and return to Minfilia in the Scion of the Seventh Dawns HQ in Vesper Bay. From there, you will be greater by the 3 runners from the different GC, and you will have to travel to the different City-States to view the speeches given by each of the GC leaders, before you can choose one and start working on getting your Chocobo.. :3