The traveler wires dont need to be labeled because either traveler wire can connect to either traveler screw terminal on the switch. To wire the new switch connect the labeled common wire to the com terminal usually bronze or dark colored on the switch.
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How to connect wire to switch. This gauge is when you want to use the quick connect method when wiring a light switch. The white wires are wire nutted together so they can continue the circuit. All that you have to do is connect the like colored wires together with wire connectors. Three 2 wire lines from a light which may be the power source. Now as for the ground wire. The green screw on the 2 way switch is for the ground so all ground wires should be connected as seen below.
Connect the black wires to the switch terminals. Simply strip the wire to the length specified and push the wire into the hole. Pull the wires apart. The switch simply interrupts the current so it. This video shows you the process in detail for connecting 2 electrical wires together. The new line is attached to a three way switch in the original box where there is a red and white wire to the switch and black to the white from the 2 wire line from the appropriate light source.
There is the existing 3 wire cable to one switch. In this picture you can see the strip gauge on the back of the switch. Connect each of the other two wires to one of the light colored traveler terminals. Trim 12 inch of insulation from the ends of the black and white cables. Connect the source wire to the bottom terminal of the switch and the other black wire to the top terminal. It is very important to connect the ground wire to the switch as well.