hard to explain without writing a lot, but ill give it a shot
start with the kettlebell in a clean position, feet side by side, hip width overlap free hand over gripped hand lunge and throw kb towards opposite hip, simultaneously retract back to starting position...
Go into a forest with a pair of kettlebells that you can swing comfortably. Find a large tree. Swing said kettlebells at the trunk of the tree in 20 second intervals with 10 seconds rest until you fell the tree. Great workout man.
Feet shoulder width apart, start with kettle bell inbetween legs (knees slightly bent, as if you were starting a kettle bell swing). From that position you use explosive power to bring the kettlebell above your head, keeping your arms relatively straight, while simultaneously straightening out your body. You should look like he-man with a kettlebell right now. Explode back down to teh start position. They're called choppers because they look like you're 'chopping wood' with a kettlebell, rather than an axe.
They can also be done from side to side, rather than going straight up, go up at an angle.
Your start position can be on the left or right of your leg, and bring the kettle bell diagonally up to the opposite side using the same movement.
I hope that helps, they're tough to put into words though.
Not to sound like an asshole, but using your method with a heavier kettlebell or even a light one would do some serious damage to the back, due to the center of mass of the 'bell'. With a dumbbell, its ok to do it with your method since the weight is distributed evenly, but with a kettlebell, doing this would create a lot of torque on the way down and cause the bell to pendulum through your legs in a bad way...
The first poster left an accurate description of how I personally do them and how I personally have seen them performed at higher levels. For your sake here's a video, though unfortunately it doesnt help the OP any further..
To answer the OP's questoin, the lunge variation detailed above is pretty accurate if you can get your head around it....