Right in the center of the Triple Triad section of the Gold Saucer there is an NPC named Triple Triad Master He is at: (x4,y7). You must be level 15 and have completed It Could Happen to You.

He'll give you your first deck of cards. As he will only give you 5 of them, it is in effect your first deck.

Once you have set your deck up (from the gold saucer menu) you should start by playing against the Triple Triad Master. You'll get your first cards that you win from him. Then as your deck gets better you can progress around the room from the NPC's with the lowest card names, on up to the Ace.

Good luck!