To throw a jump knee in Muay Thai, squat down, explode straight up, and drive your rear leg's knee into the target while keeping your hands high for defense. Master Toddy calls it "an advanced move, but actually very simple." Three pieces. Squat. Explode. Attack with the rear leg.
That's the move. The hard part isn't the mechanics.
The hard part is that you should basically never throw it cold. A jump knee with no setup is a gift to anyone who knows how to counter. You leave the ground, you're airborne, you can't adjust — and if he times you, you're going to eat something nasty on the way down.
So set it up. In the Striker's Bible, Master Toddy uses a lead push kick to shove the opponent back onto the ropes. The kick drives him, his weight shifts back, and THAT'S when the squat-and-explode happens. Push kick. Step down. Jump. The opponent is already retreating, already off balance, already covered up — and now the knee is in his face.
Hands stay high the whole time. Lead hand down at the ribs is fine. Rear hand covering the jaw is mandatory.
For the power itself, there's a partner drill straight out of the Bible. Grab your partner's head. He holds your hands tight against his neck. Your body angles at roughly 45 degrees. Now explode up and drive the knee. He gives you resistance, you build the spring in the legs. Do that before you ever try the real jumping version.
When it's time to drill the full move, partner holds the pads — lead hand low, rear hand high — gives a little resistance, and you squat, jump, rear knee. Beautiful. Time. Again.
For the standing version and the airborne variation, check out our flying knee guide. And if you want Master Toddy walking you through every knee in the system, grab The Ultimate Muay Thai Training System.