A two-gang, two-way light switch sounds complicated, but it's actually the very common two-switch light fixture you're probably used to seeing in your home. "Two-way" means that the switch has two positions, on and off, and "two-gang" means that two switches are packaged together. Typically, these switches will be used to operate two separate lights, with power coming from a common source wire.
Turn off the power going to the circuit you'll be working on at the circuit breaker. Never work on a live electrical circuit.
Remove 1/3 cm (3/8 inch) of insulation from the end of the white wire leading to the switch from the breaker. Loosen the screw at the bottom back of the switch with a screwdriver and slide the bare end of the wire underneath it. Tighten the screw with the screwdriver.
Remove 1/3 cm (3/8 inch) of insulation from the ends of the white wires leading to the lights you'll be connecting. Loosen the screws on back of the switch corresponding to each switch with a screwdriver and slide the bare ends of the wires underneath them--one wire per switch. Tighten the screws with the screwdriver.
Remove 1/3cm (3/8 inch) of insulation from the end of the black wire leading from the breaker. Remove 1/3 (3/8 inch) of insulation from the ends of each of the black wires leading from the lights. Slide the ends of these three wires into a wire nut and twist clockwise until the wires are firmly held together with no bare wire showing.