Now, once you purchase a license, you'll get a registration code mailed to you.
You then have to go to the "Restore Page", and enter your license or your email and they will mail you a second item called an Install Key. This Install Key comes as a file ending in .MJR . This is what you'll actually use to activate JRiver Media Center's license. I just tested this with a new user on my Mac. Looks like you just double click on the MJR file with JRiver closed and it installs the license. Should be pretty easy.
Welcome to JRiver. I hope you enjoy it.
Brian.