The people at NewPower99.com who sell their own replacement batteries for Kindles (I haven't had to replace mine yet, but these guys sell batteries much cheaper than Amazon) also have some
instructional videos at YT showing how to take the back of the Kindle off and on to access the battery. It looks fairly easy to do. You might want to keep this video bookmarked in case your Kindle ever falls apart again. It appears to be a cinch to snap it back together.