Ensure that the circuit breaker for the circuit powering the lights is switched to the "off" position. If the electrical board contains a cartridge fuse instead of a circuit-breaker, remove the fuse and keep it with you.
Loosen the terminal screws on the back of the switch. There are four terminals, arranged in two sets of two, with two at the top of the switch and two at the bottom.
Trim the insulation from the last 1/4 inch of each of the four wires leading to the switch. Use a sharp knife to cut all around the insulation, and then twist the separated 1/4 inch of insulation off the end of each wire.
Insert the bare-wire ends into the appropriate terminals on the switch. For example, connect the two wires from the power supply to the two terminals at the bottom of the switch, and attach the two wires to the lights to the top two terminals.
Tighten the terminal screws to firmly grip the wires. Use an electrician's screwdriver to tighten the screws until the wires cannot be tugged out of the terminals.