The Hook kick is basically an inverted Roundhouse kick. It can be executed with either lead or trailing leg from offensive or defensive stance. Bring the knee up and chamber like you are doing a side kick, but while extending the leg, whip it around and away from your body. Your leg should reach full extension near the beginning of the circular motion, and you should aim to have the kick land on target at this point also. Unlike the Side and Roundhouse kicks, there is no need to rechamber the kick in most cases, though you can do so to set up a Round kick immediately after the hook - a very popular technique.
Another way of delivering the hook kick, this time with the lead leg, is to have the trailing leg step behind the lead leg. As you chamber for the hook, your body moves forward, allowing you to close range with your opponent faster than is normally expected. Side and Roundhouse kicks can be delivered in the same way very effectively.