I have an iphone 4 which its battery ruined. I decided to replace the battery by myself. I tooke a movie about the process, I hope it’s going to help you.
There are two screws at the bottom of the iPhone. We open them with a wrench 2.5mm iPhone and then push the cover up.
In the lower left corner there is a clip of aluminum. lever it up.
There is a thiny plastic tab next to the battery, with this tab or with plastic lever you can pull the battery. ( Using the plastic lever is easier)
Install the new battery in its right place. Appendix part must be next to the aluminum clamp.
Close the clamp, put the back cover in its place, tie the screws. Now turn on your cell phone.
Attention: there is some little difference between iphone4 and 4s.