Unless I've been doing it wrong for the last ten years (quite possible! =P), each side gets hooked on the billet of the saddle to keep the pad from slipping backward. Some saddles just have pre-sewn loops that you slide on. So in the picture, you'd just unvelcro the two straps from one another, then hook each one under a billet on each side and back onto itself.
I use mine because in hard work, the pad will slip back. Even if you use the girth hooks. I've had pads half off right before I go into the dressage ring because I didn't use the billet straps and we had a last minute tack emergency :P So don't cut them off!