Hey jeebs,
It's all just mouse input. You should be able to click and drag cards onto the board. The arrows on the cards indicate which direction the card can attack adjacent cards.
Once you place a card next to an enemy card and if your card has an arrow directly facing an adjacent enemy, you have to click the enemy card to attack it.
Once a card is played, it is locked on the board, so you have to play a new card from your hand each turn.
You can also right click cards to see more stats, including race, type, class, die sides, and in some cases card ability (leader cards and some elite cards).
I'll be adding instructions directly in game likely later this month.