Welcome to Apple Support Communities.
1. FaceTime requires an active WiFi network connection.
2. You need to use an Apple ID to make it work.
3. No one else can be using the same Apple ID with FaceTime. In other words, if a family shares an Apple ID account, you each need a unique Apple ID in order to FaceTime with each other.
4. Many people have connected successfully with FaceTime after adding the Google DNS server addresses to their DNS tab in network configuration.
, System Preferences, Internet & Wireless, Network, select Location at the top, and AirPort in the left column, and click the Advanced button,then the DNS tab:

Click the + sign under any existing DNS Servers (existing server addresses are likely required by your internet provider, so leave them there) in the left column and add 8.8.8.8
Click again to add 8.8.4.4
Click the OK button to save your changes.
and close System Preferences.
Restart your WiFi network connection to be sure the change is now loaded.
And, a hint about using Apple Support Communities effectively:
You'll likely get a faster response if you post your question about FaceTime as a new topic in the FaceTime section of these forums.
The original topic here is more than a year old.
Here's a link to a related thread there:
https://discussions.apple.com/thread/3206542?start=30&tstart=0