After throwing away my fifth pair of $15 earbuds i was sick and tired of these things breaking, so when this pair broke i got out my X-Acto knife and started cutting.
Step 1: Materials
The problem spot is usually right at the end of the headphones (duh). The problem is that the wires get bent so much that they break(another duh), but this can be easily repairer with the following materials:
.different sizes of shrink wrap
.copper sheet (optional)