First remove the little plastic piece where the connections split. Strip both ends of the wire, and on the end with the jack, use a multimeter on continuity mode to figure out which wire is left, right and ground. You may have to melt off some of the insulation first.
http://wiki.robotz.com/images/6/6c/Trrs-applenonstandard.png (ignore the ipod video thing, it is irrelevant in your case.
On the end with the headphones, solder the ground wires from each ear to the ground of the jack, and left to left and right to right. Then test your wiring with this vid
https://www.youtube.com/watch?v=hTvJoYnpeRQ
After you are finished, insulate the connections with electrical tape and hot glue it together.