When you place a card, you check all the sides around it for adjacent cards and what those cards can give. Then you compare it to the card and what it likes. For every one that matches, you get +1 point. For every dislike that matches you get -1 point. You keep doing this until all 9 cards are placed.
It's an okay solitaire game and a lot of the difficulty in its creation is presenting all of the card information in a quick, simple, and obvious way. Having a list of things the card likes, dislikes, and gives, is not clear enough. You should be able to just look at it the grid and compare it to the card in your hand to have a good idea of where it can/should go.