To get the paid version of Fade In onto your computer, if you purchased it through the website, you just have to download it from your personalized download link, install it, and enter your username and registration key.
The same thing applies if you're downloading Fade In onto another computer that you personally own: just click on the your personalized download link, this time from your new computer.
(The email was sent to you from firstname.lastname@example.org, and titled "Fade In Professional Screenwriting Software user information". If you use a web-based email address like Gmail, it's easy: just search and you'll find it.
Note that if you purchased from the Mac App Store, you can simply download it (again) from the app store as long as you're logged into the purchasing Apple ID.