Audible.com now has an app (still in beta) to play and listen to audible.com audio books on android phones. The process is simple enough. Purchase an audio book first from the audible website. Then using the app on your android phone sign in to audible.com. The audio book will show up in your list of books. Download the audio book and listen.

The app can be downloaded here.

Audible.com has a collection of 75,000 audio books that can be downloaded and played on various devices including iPods.

You can download an audio book free and try it for 14 days
OR
Sign up with a membership plan which  costs $7.49/mo for the 1st 3 months and $14.99/mo afterward. With the membership you get one credit/audiobook every month.