Turn off the electricity at the circuit breaker panel. Tape a caution sign over the panel to prevent people from touching the breakers.
Unscrew the sconce canopy using a screwdriver. Removing the glass portions first will make it is easier to access the mounting screws. Pull the sconce away from the wall. You should see two wires inside the electrical box and two wires coming from the sconce. The wires should be joined with plastic wire nuts. Unscrew the wire nuts and separate the sconce wiring from the house wiring.
Assemble any portions of your new sconce that require assembly. Cut 1 inch between the insulation of the new sconce wires. Place an electrical wire stripping tool over the individual wire 3/4 inch from the wire end. Cut through the insulation and remove the insulation, leaving bare wire.
Match the positive wire to the positive wire in the house. Bring the two bare wire ends together and twist them. Screw on a plastic electrical nut to secure them tightly together. Repeat for the second wire. Wrap the wires with electrical tape to cover all non-insulated wire and caps. Press the wire into the electrical box.
Align the sconce mounting holes to the electrical box and screw the sconce into place.