You should have seen a tutorial screen when your first card battle started, you can view it again by setting tutorials to be shown again on the main menu. Remember that you can drag cards to the play area, the lighter to discard them, and the deck to increase your "cards shuffled amount" for the turn. I have plans to add more indicators for any card costs you're lacking, and mouseover tips in a patch. I'll probably also reduce the difficulty and increase the rate with which the room level decreases if you fail a card battle.