The best thing that helped me was watch how ropers and cutters kind of absorb the stop (its not the same obviously but you can take some things from it).
They really loosen up their lower back and kind of just let it sink right in there. You know when you sit in a really comfy couch and kind of wiggle your body in there tighter, think about that when you're stopping (the way you break your back), but a little more subtle.
As you're running down lean back a touch more each stride and really think about driving from the hind end.
NRHAreiner explained it really good, you aren't pushing your legs forward, more just taking them off and absorbing.
When I stop I tend to be sitting deep, and when my lower back loosen it allows me to sit deep but kind of roll my up body forward to help absorb the stop. That's my style of stopping, some people prefer to lean back more.
Here's a picture of me, the mare doesn't look awesome (I was schooling her) but its how I like to ride out the stop
The key things in stopping are really driving the hind end, getting your timing (not easy), and loosening your body to absorb it.