While the second and third generation Kindles do not have user-replaceable batteries, the first generation Kindle has a removable back cover and a removable battery. In addition, Amazon sells replacement batteries for that model. If your Kindle needs a new battery or if you want to disconnect the battery for a period of time, it can be done in just a few steps.
Lay your Kindle face down so that the back cover is facing you. Slide your Kindle's power switch to "Off" to shut the device down. Press down on the back cover and use your thumb to slide the cover to the right until it slides off.
Place your finger under the tab on the battery's right side and pull up on the tab to release the battery from its compartment. Gently pull on and disconnect the battery's connector on the left of the battery compartment.
Place the Kindle's cover on the back of your device and slide the cover to the left until you hear a click.