The ideas behind the decisions making part (or the AI) are to search every possible moves and take the best one. In each move, We assumed that the opponent chose his best move and we chose our best move. This method is "Minimax" method. As described in Wikipedia:
Minimax (sometimes minmax) is a method in decision theory for minimizing the maximum possible loss. Alternatively, it can be thought of as maximizing the minimum gain (maximin). It started from two player zero-sum game theory, covering both the cases where players take alternate moves and those where they make simultaneous moves. It has also been extended to more complex games and to general decision making in the presence of uncertainty.
The Minimax method can be applied to many other board games too. But in some complex games such as Chess, there was so many game states that you cannot search into them entirely (it would take many many years on an ordinary computer). So some heuristic must be used to approximately determine value of each state and the search must be limited at a fixed level (deeper level of search makes the AI cleverer).