Apple has released documentation that allows anyone to learn the system requirements and basic troubleshooting steps to resolve FaceTime for Mac activation, as well as usage issues.
You don’t need to wait for Mountain Lion to launch to be able to do some face-time with your friends and family. You can do it right now on a Mac running OS X 10.6.6 or later that has a built-in iSight / FaceTime cam.
You’ll further need a 128-Kbps (or better) upstream and downstream Internet connection and a working microphone on your Mac. You can even use a compatible Bluetooth or USB microphone, or even some headsets. People with multiple cameras or microphones attached to their computer need to access the Video menu and select the camera or microphone they wish to employ.
Then comes activation, which Apple thoroughly details in Support article TS4185
, and finally, the Troubleshooting. It’s a lengthy read, but also a necessary one if you plan on using FaceTime more than once.