Both my wife and I have had the same problems: phone reboots itself when opening a power hungry app like the camera, maps... So I ordered two battery replacement kits, downloaded the step by step guides and some notes to add in.
All in all, it took me about 25 minutes to complete the first one (mine, a 3G) and then much less time to do my wife's (3GS) and another noteworthy piece of advice:
When you complete reassembly and for some reason the screen doesn't seem to light up, don't panic, reboot the hard way: hold the home AND the power button down for a few seconds (10-30 seconds, you'll see when) and it will cause the unit to reboot the device. Should see screen light up.
1.) Turn off your device before beginning this replacement.
2.) Add tweezers to the tools, they will come in handy when trying to reinsert the screws and various connectors, especially #3 (ear speaker/proximi
ty) which is more like slide the ribbon back in, doesn't "pop off" like the others.
3.) The batteries were seated using a two sided adhesive tape. It's pretty strong stuff for such a small amount of tape (cut to shape) and will require a small amount of force. This is something the little spudgers aren't quite capable of dealing with. Tips broke off on mine, but I have two kits so no big deal. I suggest you use the sides of the back case and slowly, patiently, work the battery up from each side.
4.) Reassembly will go smoother if you removed the screws and set them in groups, in order to keep them organized. Reinstall using a lightly magnetized phillips screw driver (if you didn't buy the kit with tools, a small "00" size from a precision or eye glass repair set phillips screwdriver set should work).