Battle points and action points
Action points are needed in single player exploration mode. Every zone you pass through requires an action point. Battle points are spent each time you challenge another player to a duel. Consider getting the type of points which are best suited to your play style.
Cards
Getting cards is a random process. Explore the single player areas to encounter other players to earn friend points. You can spend 200 friend points to draw a random one to four star card. Merge your cards to improve them. Select a base card to improve, then sacrifice unneeded cards. You will get duplicates of cards you already own as you explore, and they will automatically level up. Combining several cards in the same attack row to activate a combo. Combos provide passive stat boosts to all your cards.