Introduction
For the official iFixit guide, follow this link. This guide has been archived for historical purposes.
This is the video guide to replace the battery in the iPhone 6, the 6s is very similar and this guide can be used.
The only gotcha is the connectors between the two halves of the phone when reassembling, the replacement process is otherwise easy.
Parts
Conclusion
iPhone 6 battery replacement is fairly easy. Be very careful when replacing the connectors between the top and bottom half of the phone. If they are U shaped or warped make sure you attach from the edge.
