You will need:
Wire cutters/strippers (I used a small pocket knife)
You may need:
A soldering aid/helping hand (see my instructable for how to make this!)
Let's get started!
Step 1: Diagnostics.
I started by taking apart the body of the headphone (it should come apart with a little light force; if not, use a thin bladed screwdriver to lever it apart). This is where the problem was for me, as the wire had come loose from the solder contacts on the speaker (see picture). If your's is OK here, it's time to break out the multimeter. Check every 5-10 centimetres of the cable for resistance, if it's fully resistant then you've found the problem. Mark the point on the cable where the problem is.
Step 2: Mending the Wire.
Step 3: Testing and Putting It Back Together.
Putting it back together: This is simple, too. Put the backing back on (this is where the superglue comes in handy). Mine also needed the little mesh grille in the front replacing; superglue does this too! That's about it really...
Thanks for reading, and good luck with yours!