Hi ! The brake works by twisting the handlebar grips. The handlebar itself sits in a yolk, and is able to pivot around in a twisting motion. The brake cable is tied to a metal loop on the handlebar, and when you twist forward, the cable tightens and pulls the brake arm and shoe down on the rear wheel. It is a barely functional brake though in even the best of times, and is really only intended to slow you down enough to regain control of the pedals which spin continuously when coasting.
And that is what the cross shaped outfit on the front of the bicycle is for. Those are leg rests, so that if you are coasting down hill, you can put your feet up there and clear of the cranks. About two thirds of bicycles built at that time are outfitted with leg rests, the other third are not, and typicially in that case, do not have brakes at all, as seen on that other later model velocipede I have. Those two components work hand-in-hand. I will say, I did try them out once, and it was effective, but it felt dangerous as all get out! I don't plan on doing that again, and when you do it you're entire body is floating four foot above the ground, at 10 miles per hour, and the stability is much less. I reckon this is further proof that people in the 1800s were tougher than today!