After purchase/rental, the video will add to the account but have a download-from-cloud icon. You can tap the video cover pic in your library/desktop, and it will offer the option to stream or download. Download speed depends on the wifi you're using and the file size. If it's a public wifi spot, you may have to wait a while if it's busy.
(If you have the 8gb HD and rented in HD instead of standard, you may need to check your memory or have a microSD card to fit the film; HD films are big.)