You have to long press on the file you want to download. Then select Save Link. It'll start to download. Select the menu icon at the bottom of the screen. Click on Downloads and the file is there.
Edit: You'll also get a notification when the download is complete. It'll appear next to your Kindle's name. Top left corner of the screen.
Last edited by SCION; 11-16-2011 at 12:27 PM.