After many years of faithful service, a circa-2003 iPod in our family had finally given up the ghost. It still worked when docked into a recharger or a Bose SoundDock we kept in the kitchen, but on its own the battery promptly went toes-up.
Luckily the market has come to the rescue, with third-party batteries allowing tech-savvy users to recover better-than-new battery life after some minor electronic surgery. The new batteries are so cheap (as low as $15) and so long-lasting (the original was 600 mAh, replacements are available up to 1100mAh) that it casts rather a poor light on Apple's own "recycling" program. There's no reason to get rid of a perfectly-good iPod once the battery is replaced; they make particularly good gym MP3 players because you're not as paranoid about scratching them.
Interestingly enough the first step is probably the hardest -- you have to use the included set of plastic spatulæ (called a "spudge" in the business) to prise open the two halves of the case, metal and plastic. The key thing to remember is that the spudge will deform or snap before either of the other two materials, so you really can't do much damage to the case. And this is how Apple itself gets into the iPods to repair them -- there's no other external door or set of screws to allow ingress.
If everything goes according to plan, the above image is what you should see. The soft blue rubber is to provide some shock absorption for the hard drive, in this case a 15 gigabyte model.
The two case halves, separated. The orange cable which connects the headphone jack and switch assembly is actually pretty fragile, so we'll need to unplug that before we go further. Lift from the male plastic assembly, rather than the small green circuit board, to avoid putting stress on the connection. A small flathead screwdriver may be useful in getting it started:
We will also have to use a small Torx screwdriver to get a small daughterboard out of the way of unhooking the battery cable, which for unknown reasons loops around the circuitry:
All that accomplished, we have the old battery out:
... and the new one installed:
I've set up this refurbished iPod to hold mostly Podcasts, and hopefully the long-lasting battery and 15gigs will mean I can leave it in my gym locker for a week at a time before taking it home to recharge and resync.