Can someone please tell me how to use cards that pop up after a battle?
There will be an in-game tutorial soon that will cover it.
You can add cards that pop-up after battle to your deck by clicking on the button under them with an energy symbol. There's a cost attached, so if you don't have enough energy (shown on the bottom-left of the screen) you won't be able to afford a new card. You gain energy by fighting monsters.