I like the card game a lot and I play it a lot but the only ones that I am missing are the ones you get from the Card Queen Quest. So how do you start it up?

What disc are you on? If you're on 1-3, go to the train station in Balamb. The Card Queen is the one standing outside the station on the right. Start a game with her using, I forget the level of the cards, MiniMog or another card on that level as your best card and lose. She will then say that Balamb is getting boring and that she is heading to another city...most likely Dollet or Deling City....
If you're on disc 4, go to the crash site on the Abadon Plains (I think that's what its called) and she'll be there. Its much harder to win cards from her there, because she uses lunar rules.....

Hoped that helped a little...

Cheers that helped a lot ive looked everywhere about it but all it says is how to get the cards and not how to start it. And thanks for telling me that you can do it on Disk 4 cuse I was gonna start again cuse of it.

The whole Card side quest was looooong, and it hurt when at the end i had to exchange my cards for items.

Yer I know but the items were quality so it had to be done (10 holy wars, 100 megaelixers)