The first priority would be to quickly pick up the vocabulary: what is a state, what is a utility function and so on.
I recently took a class on AI and we used the (rather popular) Artificial Intelligence: A Modern Approach by Russell and Norvig . I didn't actually read the book, but I've heard good things about it so it's definitely worth a look.
All the lectures for the course are available online as well. The professor my semester (Dan Klein) was a brilliant lecturer, so the lectures are worth watching if you have the time. The lecture notes are also online.
Of course, if you want to participate in this game, you are doubtless in a hurry. So you might want to skim through lectures 2, 3, 6, 7, 10, 11 in roughly that order--they seem to be the most pertinent.
In an intro machine learning course you'd learn about minimax and others, but skip paying any money and just read the basic algorithms here and look up the wiki pages for even more examples: http://www.stanford.edu/~msirota/soco/blind.html (The introduction has some term definitions.)
Edit: Also, the obligatory plug for Artificial Intelligence: A Modern Approach http://www.amazon.com/Artificial-Intelligence-Modern-Approac...