This video and corresponding article will teach you how to do the crescent kick. More specifically, both the outside and inside crescent kick.
The Inside Crescent Kick
Or as I like to call it, “the lazy roundhouse”. This is a kick that can be done with either leg, and both versions see the leg swing out and away from the centerline of the body, and then back towards the center. For some reason, some people call this the outside crescent kick-those people are stupid.
Beginning in your fighting stance, kick the leg up and slightly away from the centerline of your body (vaguely similar to the axe kick, which I will eventually do once my foot is out of the Boot). When your foot is nearly as high as it can go, suddenly torque the body towards the opposite direction of your leg (ie: if you are kicking with the right foot, torque left, and vice versa), and bring your foot towards the head of your opponent. You land with either the heel or the big toe side of the foot (the same side of the foot you’d use to kick a soccer ball).
It is worth pointing out that both types of kick are pretty much useless to attack anything but the head. This is not a problem as this kick is much easier on the hips then any other kick.
The Outside Crescent Kick
The outside version of this kick, as one would assume, is done with inverse movements when compared to inside kick: Starting in your fighting stance, bring your leg inwards towards your other leg, and then swing up, over, and out towards the opponent’s head. This one is weaker than the inside crescent kick, but must be learned to learn the spinning crescent kick.