There are whole libraries dedicated to AI, this document just covers the absolute basics. Before looking at the various methods, I need to say this :
Computers Are Not Intelligent !!!! (They just like us to think they are)
The goal of artificial intelligence is to fool the human opponent into thinking that their opponent is intelligent, not to actually create intelligence. Most artificial intelligence are simple algorithms which try to mimic human behaviour within certain rigorously defined boundaries. AI is an art-form, and often the simplest ideas are best.
The following methods can be used in games, but most commonly, games use a hybrid of approaches, borrowing from various methods. Please note that I have deliberately avoided mentioning randomness. Some patterns may be generated randomly, but in general, the only other time you should use randomness is when you have made your AI virtually unbeatable (which let’s face it, is never).