How do you remove insulation from headphone wires?

Usually, you can remove laquer by melting solder onto the wires

I've used a microtorch to burn off the insulation with a lot of sucess - use the microtorch on the tip of the wire, and let a little more burn off on its own and you're good

On smaller, thin wires, simply applying heat from the iron will delaminate (ie, remove insulation from) the wire. I've done this (by accident - creates interesting situations in a wiring harness if you are lame like me and try to shrink heat-shrink tubing with an iron - don't do it!).

You might be able to use a chemical agent to strip the insulation too.

You could also try a razor blade, but you need ninja-class hand-steadying abilities.