The CC group quest can be initiated after the Garden fight in disc 2 (the NORG vs. Cid stuff). You need to have won a certain amount of card battles in the Balamb area (i.e. Balamb town and Balamb garden). I haven't heard an exact number, but 15-20 should be enough. Talk to the SeeD often standing to the right of and slightly behind the directory in Balamb Garden, who usually talks about the CC group. If you've won enough battles, and are far enough in the story, he will reveal that he is CC Jack, and challenge you. After beating him, you can take on the other ones in order.