Apple's official website has a short tutorial on how to use FaceTime while behind a Firewall. As the article states, FaceTime normally starts up without a hitch. However, joining a network behind a firewall, such as one at school or work may cause problems.
Here's the fix, taken directly from Apple's official website:
Ports to open
If the Wi-Fi network router that you are connected to uses a firewall or security software to restrict Internet access, contact the network administrator and reference this technical article. To use FaceTime on a restricted Wi-Fi network, port forwarding must be enabled for ports 80, 443, 3478, 4080, 5223, and 16393-16402 (UDP).
Depending on the NAT configuration for the router and network, additional ports may be used to send and receive video. Some router-specific features or configurations may interfere with FaceTime. This includes port mapping on either end, SIP dropping, or dynamic opening of media ports.
The Wi-Fi network administrator can refer to their router, firewall, or security software documentation for information on configuring port forwarding.
If you encounter issues using a Wi-Fi network, use standard Wi-Fi network troubleshooting to resolve interference and other issues.
Need some help using FaceTime? Check out our tutorial: Here