There are two ways to download an audiobook:
1. If the title wasn't previously played, go to your Library, and click on the file title or image. The first time you select a title you will be asked if you wish to download or stream the audiobook.
2. If the audiobook has previously played, click the audiobook menu icon from the library or now playing page. You will open a menu from which you can choose "Download to Device". Once the download started a progress bar will appear indicating the download advancement. After the book has finished downloading, a cloud icon will disappear which means the book is now stored locally on your device.