The left hook is the most difficult punch to learn. Unlike the jab and straight right, the left hook has mysterious nuances that simply take time for most boxers to discover and assimilate.
Most beginners think the left hook is some sort of sweeping, round-house punch thrown and powered by a loopy left arm.
The hook is an inside power punch. It’s most effective when you are close to your opponent. The punch begins with a weight transfer to your left side. From the guard position the left elbow is brought up, almost parallel to the floor, so that the arm forms a sort of hook (literally). At the same time the fist is rotated wither palm down for a very close target, or palm-in for targets farther away.
While the arm is held as described above, the punch is delivered by pivoting left foot, left leg, and torso sharply to the right in powerful, one piece torquing action. The arm does not move independently of the whole. Like  a gate sweeping around hinged posts, this punch is powered by leg, hips, back and everything else in the barn. When it is thrown properly, it’s one of the mighty weapons in boxing and it is held in a very high esteem.
Think about crushing peanuts with the balls of your left foot as you swing it around and think ‘ Hey buddy!’ as you bring the punch to completion by tucking it into your chest as if you are hugging him around the neck.
Like all punches, the hook accelerates as it tracks to the target, the fist clenches before impact and is sharply returned to the guard position along with everything else that went for the ride
Recovery is very important after the hook. Punches never hang, they snap!
Think acceleration, SNAP, recovery.

Please check this great video on how to throw the left hook PROPERLY.

http://www.youtube.com/watch?v=gmLYvJON_OU