First of all, you need to win about 100 card games in the garden (which is
difficult to do without decreasing your SeeD rank) The first member appears at
the directory board, where the first guy tells you about the card club. Careful,
every one of these players can be difficult depending on the rules you are
using.
Once you beat the first guy, the others appear one by one. I'm not sure who
comes next but it's either the diamond princess duo (the two girls who are
always standing at the directory where you find the first guy) Or it's the
coloured man who appears walking slowly past outside the entrance to the dorms
and the garage. Either way, defeat one and the other appears.
After these, look in the hall where the guy first gave you the 9 cards on disc
one. Now, it's either him or the guy next to him, try them both. The next player
is Xu, keep playing her even after you beat her as she has the Carbuncle card.
Before you go looking for the CC king, try the training area, the guy that's
sometimes standing there is the CC joker and has a Leviathan card. You won't see
him if you use "Encounter None" so you'll probably have a few scraps with T-rexaur.
Go to Dr Kadowaki, She'll tell you that she used to be CC king but lost her
title. Beat her and head for the dorms. Keep taking a rest and eventually
Quistis appears in your room to challenge you! She has the Gilgamesh card, worth
10 Holy Wars.
Finally, if you don't get all their rare cards but you beat them, they will all
be aboard the Ragnarok on disc 4!