join a tournament

To join a tournament, go to a card lobby desk and pick the second option, then pick the tournament you want to join. Finally pick your slot, then wait around and your be transported automatically to the tournament battle.

watch someone else in a tournament

To watch someone else in a tournament, talk to the card lobby desk and pick the 3rd option, then the second, then the second. Then name a game, and say ok. You'll then be watching that tournament battle.