First you will need to get a composite to four pin 2.5mm cable. This cable is supplied with the original GoPro, however, you can also purchase it from ebay or amazon. Be sure that the cable has a 4-pin 2.5mm jack.
Next you will need to remove the thick plastic plug from the end with the jack. This can be most easily accomplished using a hot knife or heating a hobby knife with a torch. After cutting away the black plastic you may find that the jack is encased in a separate layer of plastic that resembles wax. This can also be cut or melted away, however, if you decide to melt this away be sure not to overheat the jack because the insulation between each of the pins will burn or melt away. After removing all of the plastic, the old wires can be desoldered from the pins just make sure not to apply excessive heat. You will be left with the core of the jack, it should resemble the picture below.
Check the connections between the plug side and the wire side to be sure that they match the connections above. This can be done using a voltmeter and testing for the continuity between each of the rings and solder joints. You want to be sure that you solder the new wires to the solder joints that correspond to the diagram of the rings above.
Finally you can attach whatever plug you would like to the end of your wires, I prefer to use a 3 pin futaba connection with ground, audio and video pins. Wrap the plug in several layers of heat shrink to protect the wiring and solder connections. It can easily be attached to a video transmitter or removed when not in use.
Another option is to make the entire plug into an adapter such as the following.