My battery of my 3G was not dying, it was pretty much dead already. As soon as I hit the web (with a fully charged battery) the phone shut down. Calls were only possible for 10 minutes, then the batterie died again
Following the step by step guide on iFixit, it was a piece of cake.
The steps were perfectly described and the pictures showed exactly what to do next.
I only learned not to use too much force when trying to remove the screen. I finished step 2 and three with one pull...
Luckily the cables came of smoothly.
Removing the battery was the biggest challenge. It was clued so tightly to the cover that I almost broke the spudger. Next time I go with the professional version...
Reassembling it was quite easy. In about 30 minutes I had a new battery and finally the phone is usable again.
Add the separate spudger to the shopping cart, its worth the extra buck.
I will now repair all my devices myself before I go and burn my money on apple repair service :-)