My iPhone 4s battery is going low after 2.5 years of daily use.
After reading through this manual and all comments, and watching a youtube video (http://www.youtube.com/watch?v=RW8RSA51V...), I finished it without a glitch in 10 minutes. Powered right back up and found the carrier.
Be sure to power OFF the phone before you start.
Going through this video before starting is very useful. It shows you how to deal with the black grounding piece, which is a lot easier watching it in a video than in pictures.