Upgrading a theme from Free to Pro is similar to installing a theme. If you have made any PHP or CSS changes to the free site or if you want a more thorough walkthrough of upgrading, you can view this document: http://slocumthemes.com/docs/upgrade-wordpress-themes-free-to-pro/
You will find the Pro theme file that was emailed to you in the contents of the email (check your spam folder if you do not get the email) and download that file to your computer in .zip format. Leave it in that format and navigate to Appearance > Themes > Add New.
From here, you will select the zipped theme file from your hard drive and select "Upload". If you choose to activate the theme after upload, this will make the Pro theme your new theme. Congratulations, you have upgraded!
If you have any additional questions, please let us know!