Use this guide to replace a worn-out battery on your 2nd generation Touch. This procedure requires soldering.
First make sure that you actually need a new battery. Many iPod Touch Generation 2 users experienced major reductions in battery life after upgrading from 3.x to 4.x of the iPod OS. If your battery life problems coincided with an upgrade to 4.x check out this thread on the Apple Support Forum first. [http://discussions.apple.com/message.jspa?messageID=12407219#12407219|Low battery life on iPod touch after installing iOS 4]