It’s memetic fame aside, the roundhouse is a kick you ought to be learning: it’s relatively quick, non-telegraphed, and hits all targets hard, from the ankle all the way to the head. However, the beginner will often do a sort of low crescent kick (hitting with the side of the foot) which is significantly weaker than the true roundhouse kick. You can watch the video below for instructions on how to tell the difference and roundhouse kick properly, or read textual instructions below the embedded Youtube file.
To throw the roundhouse kick, you begin by whirling the hips, and then sort of “unleash” the leg, don’t just flail the leg.
Consciously turn your leg so the front of the tibia hits, or the instep, NOT the talus bones of the ankle. As always, look at where you’re aiming, that keeps all of the motions focused. Fully rotate the leg to land clean, do not roll the tibia (consciously think to rotate your leg AND your foot, also angle the foot so it’s flat.). As you whirl the hips, SIMULTANEOUSLY rise to the ball of the foot of the standing leg (which will be the forward leg), and look at where you land. If you feel crippling pain, you did it wrong. Also, your torso must turn, if your torso is 45 degrees away from where it started, that’s good.
As stated above, land with the flat of the foot or the shin.
All in all, a bit more complicated than the previous kicks, but manageable