Basically you have colored enamel wires for gnd containing the signal wires.
Each one of the three signal cable are covered with a external layer of insulated wires as described by @whatusername.
The colouring of the cables is the following:
* Left audio: Red cable, coated in green enameled wire.
* Right audio: Black cable, coated in blue enameled wire.
* Mic: white cable, coated in gold enameled wire
The copper inside the red, blue ang white cable are still mixed with plastic fiber so my suggestion is to use heat for remove the insulation from the enamel and to remove the non metallic portion of wire before soldering.
I manage to do it with a fast passing flame from a lighter but I'm sure a heat gun will do a lot better work.