The Kindle has a built in mp3 player that you can use to listen to music, podcasts and audio books. To make use of this feature, upload your files from your computer to your Kindle.
The mp3 player can be found on the Experimental page of your Kindle. The +/- key on the right side of the Kindle controls the volume.
Advanced Tip: You can use shortcuts to control the mp3 player. Alt+spacebar will stop or play a file. The ‘F’ key will skip to the next track.