I suggest you look at this game of Reversi I built a few weeks back for fun in Flash. This has a very basic AI implemented, but the basics could be applied to your situation.
Basically, the way that game works is after each move (player or CPU, so I can determine if the player made the right move in comparison to what the CPU would have made), I create a Vector of each possible legal move. I then decide which move provides the highest score change, and set that as best move. However, I also check to see if the move would result in the other player having access to a corner (if you've never played, the player who grabs the corners generally wins). If it does, I tell the CPU to avoid that move and check the second best move and so on. The end result is a CPU who can actually put up a fight.
Keep in mind that this is just a single afternoon of work (for the entire game, from the crappy GUI to the functionality to the AI) so it is very basic and I could do things like run future possible moves through the check sequence as well. Fun fact, though, my moves (which I based the AI on obviously) are the ones the CPU would make nearly 80% of the time. The only time that does not hold true is when I play the game like you would Chess, where your move is made solely to position a move four turns down the line
For your game, you have a ton of variables to consider and not a single point scale as I had. I would suggest listing out each thing and applying a point value to each thing so you can apply importance values to each one. I did something similar for a caching system that automatically determines what is the most important file to keep based on age, usage, size, etc. You then look at each card in the CPU's hand, calculate what each card's value is and play that card (assuming it is legal to do so, of course).
Once you figure that out, you can look into things like what each move could do in the next turn (i.e. "damage" values for each move). And once that is done, you could add functionality to it that would let the CPU make strategic moves that would allow them to use a more powerful card or perform a "finishing" move or however it works in the end.
Again, though, keep it to a simple point based system and keep going from there. You need something you can physically compare, so sticking to a point based system makes that simple.
I apologize for the length of this answer, but I hope it helps in some way.