To use FaceTime on a restricted Wi-Fi network, port forwarding must be enabled for ports 53, 80, 443, 4080, 5223, and 16393-16472 (UDP).
Most routers will "just work," but if you're having issues it is worth a check. In my experiences my home Belkin router didn't need any tweaking and each time I've used FaceTime from a public WiFi Hotspot it also worked swimmingly. If you're not sure it's all working and need a test, don't forget you can call Apple and talk to a real person via FaceTime at 1-888-FACETIME.
Apple iPhone 6s