With the basic rule of Open in play you can see all of your opponent's cards from the start. This means you can predict what cards he will lay down where, and can attempt to counter these moves. Before laying down any card, you want to know whether or not your opponent will be able to flip it. Look at their cards to see if the opposing edges are higher than yours. If you see that they can in fact flip your card, look at your own cards to see if you would be able to flip it back.
Many players try to play defensively by choosing cards that only have one low value edge, but you must remember that this means that the card may very well only be flipped once. If your opponent manages to flip it, make sure that you have a card that can flip it back. While it is tempting to open strong, it is best to save your most powerful cards for the end of the game. For example, in most games you can play Ifrit in the bottom middle and none of your opponents cards will be able to flip him. While this starts you out "safe", it takes away your ability to save the day should things go wrong towards the end of the game. It is better to use weaker cards to try to bait your opponent, then seal the deal with Ifrit at the end.
As you travel the world throughout the game, you'll learn various rules and variations effecting how the game is played, how cards are chosen, or how cards are traded. Learn all about these in the FF8 Triple Triad Rules Guide.