Turn off the electrical current to the room. Spread out a tarp to catch sawdust when you cut into the wall. Cut a small rectangular hole in the wall for the new floating receptacle, using a jigsaw. Thread electrical wires that are connected to a power source to the hole.
Strip the electrical wires with a set of strippers or pliers so you can access the copper wiring. Be careful not to accidentally cut the metal wires as you are stripping them.
Connect the electrical wiring to the receptacle by wrapping the wires around the silver and brass terminals. Attach the ground wire to the ground screw, the black wire to the brass terminal, and the white wire to the silver terminal. Bend the exposed copper wires into place around the terminals, using pliers.
Push the electrical receptacle into the hole. Cover the outlet with a frame that matches the room. Using a screwdriver, attach the decorative wall plate to the outlet and the wall to hold the electrical receptacle in place.