Ok, keep in mind I haven't been doing this a tremedously long time (about a year), and my experience with kicking in other arts is severely limited, but here goes:
We're going to assume a left lead stance and you will be kicking with the rear (right) leg. First off, take a step (or hop) about 45 degrees to the left from straight ahead, to your opponents right. Now, your support (left) foot will pivot outward, ideally ending with the heel pointing at your target. The foot should be flat on the floor to provide max stability. As you pivot, turn your hips, kind of like you are turning around to look behind you, but don't actually go that far. While your hips are rotating, your kicking (right) leg will lift off of the ground. Let it swing, like a baseball bat, at the desired level (thigh level is good). Don't tense your thigh muscle, just relax and let the kick make contact. You should be hitting with your shin, not the foot.
About halfway through the kick (experiment for the right timing), drop your right hand back behind you, this adds counter balance to the movement so you don't spin like a top (unless you want to). Be sure to keep your shoulder up to protect the chin though, otherwise a counter punch has your name on it.
On contact the knee should be bent, and the force of the blow should contact the target at about a 45 degree angle inward (not straight in from their left side - 90 deg. - and not straight in from the front - 0 deg). Again, don't tense up on impact, just let it swing like a baseball bat or axe, right on through the target.
That was a little longer than I thought it would be, but I hope you can understand that. If you have any questions or points you need clarified, just ask. I'm sure IFAJKD has been doing this kick for awhile also, so maybe he can fill in any gaps here.
To sum up, the major points - support foot is flat, hips completely turn over (the biggest problem with newbies), the hand is dropped to provide torque, but the shoulder be kept up for defense, and don't chamber the kick, just let it go. I'll look around and see if I can find any good clips online.
[edit]forgot to address the hand issue[/edit]