You need to have enough of the various resources as well - it's been a while since I played, but if I recall correctly it's mana and energy. Then click the card and point to the target, when you see a thin dotted line, click and voila. Also your turn is infinitely long, so you can replenish the resources by using consumables and keep going until you've used all your cards or have won. The collar to capture them has an x% of working depending on their remaining HP.
But honestly you won't have many actual fights, just put down 4 spike traps in a row after the entrance and any invader will drop dead before reaching you.