As you've discovered, earbuds don't last all that long. An inexpensive pair of earbuds will usually fail sooner or later, either where the cable meets the phones or where it joins onto the jack plug.
The good news is that chew-through at the plug end is relatively easy to repair -- you just need to attach a new plug to the existing (now shorter) cable. For starters, you need a knife or scissors, a match, and a soldering iron. You will also need a 3.5mm stereo jack plug.
Preparing the cable
A headphone stereo cable has two cables running through it, one for the left channel and one for the right. These are usually colored red and green. Each of these cables is surrounded by copper wire (the ground).
1. Strip the red and green cables back so you have about a half inch to an inch of bare wire.
3. Strike a match and briefly heat the ends of all three wires to burn off any insulating covering. If you don't do this, the wires won't make a proper electrical connection and your headphones won't work.
Attaching the cable to the plug
Unscrew the case of your jack plug and you'll see the three terminals for the three wires in your cable.
If you get the red and green wires mixed up, your headphones will still work but the left and right channels will be switched over. It can be quite tricky to support the jack plug while you're soldering it.
Some words of warning: Don't hold the jack plug while you solder it. The heat will rapidly travel through the electrical pins and burn your fingers. Also, make sure the three wires are well clear of one another when they're soldered. If they touch anywhere, you'll either lose sound in one or both of the headphones or get mono instead of stereo.
That's all there is to it. Hope this helps.
