On the back of the caliper you'll find a bolt on either side. It will either be a hex bolt of an Allen bolt. Remove these two bolts and put them aside.
Hold the caliper from the top and pull upward, wiggling it around to loosen it up. If it's stubborn, give it a few taps (taps, not Hank Aaron swings) upward to loosen it a bit. Pull it up and slightly away, being sure not to put any stress on the brake line (that black hose that's still connected).
If there is a place to safely set the caliper back there, do it. If not, you'll need to take your bungee cord and hang the caliper from something, the giant coil spring staring at you is a good spot. Don't let the caliper hang by the brake line, it can cause damage and lead to brake failure!