CARD UPDATE
Thanks to the Ifrit Card I got after beating Ifrit, I could now go ahead and challenge the little kid in the blue shirt running around Balamb Garden. It may take you a couple of tries (make sure you save first, so you don't lose your Ifrit card!) but you can win MiniMog from him! He might take a few tries before he plays it, too.
With MiniMog and Ifrit, go to the cafeteria and challenge the guy to the far right to a game of cards. HE has some higher level cards that you can get with some practice. Eventually he will play the Quistis card. With Ifrit, MiniMog and some other cards you'v picked up, you can beat him, although it will be a challenge. Always save first.
Now with these three cards you should be able to beat pretty much everyone in Balamb Garden. So far, you don't have the abilities to actually DO something with the cards, (you need Card Mod and different RF abilities for that), but the card game is really fun, so run around playing people and grab cards. Some cards to look out for that gives you great magic in the future are (taken from ABrea's Power-Up Guide and Sister's Card FAQ on GameFAQs:
10 Ruby Dragon -> Inferno Fang -> 20 Flares (F Mag-RF, Ifrit)
Abyss Worm -> Windmill -> 20 Tornados (I Mag-RF, Shiva)
Tri-Face -> Curse Spike -> 10 Pains (ST Mag-RF, Diablos)
Armadodo -> Dino Bone -> 20 Quakes (Time Mag-RF, Diablos)
2 T-Rexaur -> Dino Bone -> 20 Quakes (Time Mag-RF, Diablos)
Gayla -> Mystery Fluid -> 10 Meltdowns (ST Mag-RF, Diablos)
10 Chimera -> Regen Ring -> 20 Full-Lifes (L Mag-RF, Siren)
Cockatrice -> Cockatrice Pinion -> 20 Breaks (ST Mag-RF, Diablos)
Belhelmel -> Saw Blade -> 10 Deaths (L Mag-RF, Siren)
Tonberry/King -> Chef's Knife -> 30 Deaths (L Mag-RF, Siren)
Forbidden -> Betrayal Sword -> 20 Confuses (ST Mag-RF, Diablos)
Elastioid -> Steel Pipe -> 20 Berserks (ST Mag-RF, Diablos)
5 Turtapod -> Healing Mail -> 20 Curagas (L Mag-RF, Siren)
5 Torama -> Life Ring -> 20 Lifes (L Mag-RF, Siren)
T-Rex/Armadodo = Dino Bone = Quake
Blood Soul = Zombie Powder = Zombie
Gesper = Black Hole = Demi
Wendigo = Steel Orb = Demi
Blitz = Dynamo Stone = Thundaga
Snow Lion = North Wind = Blizzaga
Mesmerize = Mesmerize Blade = Regen
Abyss Worm = Windmill = Tornado
Tri-Face = Curse Spike = Pain
Funguar/Bite Bug = Magic Piece = Esuna/Cure/Fire, etc.
Buel/Jelleye = Magic Stone = Haste, Slow, Cura, Fira, etc.
Vysage/Imp = Wizard Stone = Curaga, Firaga, etc.
When you have L-Mag-RF, buy stuff and refine:
Tent -> 10 Curagas (L Mag-RF, Siren)
Cottage -> 20 Curagas (L Mag-RF, Siren)
A lot of the items you can get from Card Mod is also usable on Quistis to give her different Limit Breaks.
I'm gonna go crazy on playing Triple Triad now.