The box jump trains a quick and powerful reactive force in your lower legs and hips, perfect for maintaining momentum between multiple techniques in a complicated environment.
1.) The technique I often use is a box-jump/depth-jump cobo. If you are relatively untrained or have any possible injuries, a regular step down from the box would be indicated. Stand in front of the plyo-box or other object you are using for a platform. Your feet should be directly below your hips.
2.) Crouch down, bending at your hips and knees into a partial squat, swinging your arms behind you.
3.) Explode upwards, coordinating the swing of your arms with the extension of the hip to maximize momentum.
4.) Tuck your knees and hips, spotting your landing on the edge of the box. Fully extend the hips at the top.
5.) Jump backwards slightly, making sure to clear the edge with your shins and knees, but minimizing the height you gain off of the box.
6.) Spot your landing, absorb with your toes first, flexing at the ankles.
: notice, minimal knee bend.
7.) With minimal knee bend, explode immediately back onto the box. This should be a function of your hips and calves more than your quadriceps.
: The power from the jump is a function of a powerful hip extension.
8.) Pause and repeat. If you have a history of overuse injuries in your knees/lower legs, or you are relatively new to training, a step off the box into a powerful jump would be more appropriate. The goal would still be to cycle them as quickly as possible.