Have you looked at the tutorial menu? There's a pretty good description of the game in there. Also, if you don't understand something about the card game, the best way to learn it is to save the game and just try. If something horrible happens, reset, reload, and try again.
It is pretty simple: Everyone has five cards to play with. The number on each side of a card tells you the "strength" it has there. It goes from 1 to A (A is the highest, of course). If your enemy puts a card (his colour is red) with the value 8 on the right side, every (blue) card with a number higher than this on the opposite side will beat that card and add it to yours. There are also special rules like "Plus" (I think that this was the name) which said that putting a card matching the corresponding numbers of two (or more) cards lying beneath it will turn them to yours.
There are much more rules, the easiest thing might to simply try it out for yourself.