Each player holds his deck where the other player can't see it, and plays one card at a time. You play the cards at the same time and compare their SCORES.
The card with the higher SCORE wins each "battle."
If the winning card is a CARNIVORE, it EATS the other creature . . . remove the losing card from play. The winning card goes back to the winner's deck, on the bottom. If it is not a carnivore, it captures the other card, and the winner puts both cards on the bottom of his own deck.
But if neither card is a carnivore, or both of them are, then the battle is really a tie. In that case, each player must play out two more cards without looking, as "ante." Then each player plays a third card and compares their scores. The winner of that battle captures the two original cards and each player's "ante." (This way, a player who has a powerful card can still lose it.)