After Squall wins 15-20 Card Battles in Balamb Garden, the Card Club Quest becomes available. Now you can do Card Battle with various members of the CC Group in Balamb Garden. Here are their locations and the order in which you should challenge them (some appear randomly. If they’re not where they should be, try leaving the area and re-entering):

Jack He wanders around the Garden Directory Board on 1F.
Club He wanders the northern regions of 1F.
Diamond Two girls both stop to chat at the Directory Board.
Spade A man near the lift on 2F. He doesn’t appear too often.
Heart Xu on 3F Command Bridge.
King Speak with Nida after defeating Xu, then talk to Dr. Kadowaki at the infirmary using [Square]. Head for Squall’s cabin and ask your companions to leave you alone. Choose to rest, and during the night, King will appear randomly. If you fail to win, you can have a rematch on the 3F Bridge.
Joker In the Training Center or near the Blizzard DP after you defeat Jack. He also sells items.

If you haven’t won it already, the kid in blue circling the 1st floor holds the MiniMog Card.