When you purchase Evolved Caching, you will receive an archive of the extension along with licenses for the domains you have told us about. Extract the contents of this archive to the root of your Magento install, and you will see that a file has then been added to site root called evolved.php. This is the gateway to the extension and to use it, you need to make a couple of changes to the file .htaccess, also at site root. Open this file and change all instances of index.php you find to evolved.php - there should only be two (plus one comment that you don't need to change).
That's all you need to do to install the extension!