After completing your order you should receive an email containing a download link for the PRO version.
You need to download a ZIP file which is the theme package (you don't need to expand it as you will need it as a ZIP file).
Once you downloaded the package, you need to go to WP admin -> Appearance -> Themes -> Add new and click the "Upload theme" button at the top of the screen. Then you have to select ZIP file you downloaded and click install.
Then, when prompted you have to activate the theme.
The PRO theme is a child of the free theme, so you only need to upload and activate it without removing the free theme and the companion plugin.
So when you look Appearance Theme you will see this:
Click on Appearance --> Customize to double check that it is on PRO Theme.