First, turn off the power to this circuit to avoid getting a shock.
If the two devices that are controlled by the combination switch are lights, you will want to join the two (2) white (neutral) wires together with a wire nut, as these are not connected to the switch.
You also want to connect the bare copper wires (ground) together and connect one of them to the switch's green grounding screw and IF the wall box is metal, you also need to attach the ground wire to the box with a green grounding screw.
Now, you can connect the wires that go to your lights, the red and black wires that are part of the same wire and are routed to the same location thru the wall box. Take either the black or red and connect them to the screws on the side of switch that are not connected together with the small brass strip between them. Put the red on one of these screws and the black on the other.
Now with the black wire that is the hot (Common), this is the one that is bringing power into the wall box, should be connected to the other side of the switch, the one with the two (2) screws that are joined together with the brass strip between them.
This will allow you to turn on and off each of the lights (or a fan, etc) separately with each switch sharing the common power source.
Here's a picture of the switch that shows the side of the switch with the common side and the brass strip that connects the screws together. This is the side where the one black (hot / common) wire that supplies the power gets connected.
You can also open up the box the switch came in and you'll find a wiring diagram for the switch that illustrates how to properly wire the switch for your application.
I hope you find this Very Helpful and best regards!