Quote: "Yeah, I figure once the mods see this it'll be locked. I tried twisting the ends together though, and it didn't work. I suppose i could try again, but since it's a headset it may be a bit more sensitive."
As VanB Said, you need to carefully scrape off the colored coating on the wire until you are left with the copper (A sharp knife will do it), then twist them together.
You will find that when you start trying to scrape off the coating, the wires will start to unravel and break down. It would probably worth dabbing a bit of superglue on the end of the wire to prevent this. You will be able to scrape off more coating and get a better contact this way.
It would probably be worth getting some heat shrink tape or electrical tape to bind it all together.
If you are able to get a good amount of surface contact between the repaired wires and no short circuiting, your headset should work again.