My iPhone 3G was handed down to my wife when I got the 4. It had been working great, until its WiFi ceased to function. Consulting the Oracle of Google led me to suspect that the problem was fractured solder joints, and an trip into the oven was in store for the motherboard...
So why a battery? The phone was a launch day 3G, and will likely go to my daughter to function as an iPod Touch when the iPhone 5 comes out (wife will take the 4 at that point). Since I had to disassemble the phone to get the motherboard out, I figured I may as well replace the battery, as it was nearing its end of life, and had begun requiring a topoff charge if I left WiFi and Bluetooth on...
The process went fairly smoothly. I was already experienced in the dissection of iPhones, having previously shattered (and subsequently replaced) the screen of my 4. I used the ifixit app on my iPad as a reference, and HIGHLY recommend it! It was very clear. Disassembly took roughly 10 minutes (going slow and careful), until I got to the old battery removal. That thing was stuck down like you wouldn't believe, but another 15 minutes and some coaxing with a hairdryer allowed me to finally get it out of there. I was waiting for the mobo to cool, so I had the time... Reassembly took 15 minutes and a couple of tries - you must be very careful and ensure that everything is seated just so. It's not particularly difficult, just tedious.
Use ifixit's guides - they are fantastic! Reassembly is just the reverse of disassembly, so don't panic when you can't find the "How do I put it back together?" guide.
Lay out a soft cloth on the table where you are disassembling. Not only will this prevent scratches (on both device and table), but those itty bitty screws bounce like mad when they drop accidentally and hit a hard surface! The cloth will help control that, so you're less likely to lose any screws.
Have numerous containers handy to hold your screws separately, and label them. Yes, it slows you down, but you want to make sure you get the right screw back into the right hole! I label my containers with the ifixit guide step where I removed them, and if there's more than one screw type/length, I'll separate those into different containers as well.
If there's anything you can't quite understand from the static images (wasn't the case for me on this one, but I can see other devices being a bit more tricky), there are countless teardown videos on YouTube. Find one (or more) and take the time to understand it before you rip into things.