Any exercise's technique will depend on what you want to get out of the lift, but most of the time, you'd sit down to the box fully, but not releasing the tension throughout your lower body, before powering back upright.
If you squat down onto the box and then "take all the weight off your legs", you'd be transferring the load off the muscles and directly onto the spine which is a hyoooge invitation to injury.
You can either use a very brief pause before ascending, like if you just wanted to be sure of your squat depth on each rep, or you can use a longer pause on the box while maintaining that full body tension, to eliminate the stretch reflex and build explosive strength.
Thib's talked about this method in his Box Squat for Bodybuilders article:
I think it was actually Big Tony G who wrote about it in this article:
It also has some videos of what he's talking about.