For the most part you can only get new cards from quests. There is one card available in New Targonor that doesn't require a quest, just purchasing a random amount of drinks from an NPC and drinking them until you learn the card. In the future there will be altars of Kaerellun which will enable you to do turn ins for cards.
You can find a list of quests here:
http://www.vgtact.com/wiki/index.php?title=Main_Page
For the card mentioned above, do a search on the wiki for mixmaster.