The Kindle eReader comes with a charger and depending on the battery age and type, the charge should last somewhere between a few hours and a few days of use. A Kindle battery not charging when plugged in could be faulty or have a software problem. Alternatively, it could be the charger's issue. Any of these problems are fixable.
Connect the charger to a different outlet if using a wall outlet, or a different USB port on your computer if using your computer. If that doesn't work, add or remove the USB-wall port portion of the cord and switch to the wall outlet or computer to try something else. Check the bottom of the Kindle for the charge light. If the charge light doesn't turn on when plugged in, the cord or USB-AC adaptor needs to be replaced.
Restarting the Kindle helps resolve some kinds of issues. It's a good step to try when encountering problems. Press the "Home" button, then click "Settings," then "Restart."
Trouble holding charge
Turn off wireless and 3G if applicable. These drain the battery life more quickly. If you're having trouble charging, make sure these are off before beginning the charge.
Call Amazon's Customer Service line if your USB-AC adaptor needs replacing, or if none of the above steps has helped and you believe your battery is faulty. There's a one-year limited warranty that may cover replacement of parts or the entire Kindle. The number is 0800 496 1081.