The most common method is to use the strengths of computers (target recognition, reaction time, angle computation, etc.), and then apply a bit of randomness or latency to the decisions or results. Doing it this way, you can amplify the handicap based on the difficulty settings (if the game has them).
A better method is to monitor how well the player or players are doing, and then adjust the accuracy on the fly to keep them barely winning. A simple example would be racing games. Once you teach the AI to successfully navigate the track, it is easy to tweak the controls or the car’s properties so that the AI can stay right on the player’s tail, and occasionally pass them to keep it exciting.
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