Nothing is 'guaranteed' to work but this is the proper way to handle this situation.
Let me put it to you this way. I use AirPort routers exclusively and without having to 'open ports' FaceTime works without any problems on all my devices, Mac as well an iPhone.
If you insist on trying the 'open ports' method the 'Configure Port Mappings' button on that screen is where you do it. Be aware that doing it this way creates static maps so the ports you open can only be mapped to one IP address at a time.
Here is a list of port used by Apple software: Well known TCP and UDP ports used by Apple software products
Ideally you want to let NAT-PMP handle it because it allows the ports to open dynamically, on demand, by the devices and software that request the ports.
If enabling NAT-PMP does not solve your problem then the problem and solution exists elsewhere.
Yes, double NAT means that you have two routers one behind the other that are providing DHCP and NAT service. You need to configure only one router to provided those services or you may expereince other network problems.
In your case I'm guessing you have a modem/router provided by your Internet Service Provider that is making the primary connection to the Internet and providing DHCP and NAT and you have now also configured your AirPort router to also provide DHCP and NAT. If you want the AirPort router to provide DHCP and NAT then you need to turn off those services in the other router. That will solve the double NAT error.
Of course, the Clearwire modem that I have has many threads that complain about you not being able to shut off NAT on it. I ended up ignoring the warning in the router and things seem to be working fine. I can FaceTime and iMessage no problem.
Thanks for your help! I would give you a "solved" if I could.
Thanks for the help so far for all of us in this situation. My case is somewhat similar but half way there to a solution. Sniffle is right, they upgraded Airport utility UI and it's quite different from the screen shot you have above but I was able to find the page and mine is set to 'DHCP and NAT'.
But my issue is that when someone calls me via FaceTime and I accept it, it freezes up. I can hear the caller but the view remains frozen. On the other hand, it works perfectly when I call out. So my problem is receiving facetime calls. Any ideas what to do?
Thanks again for your time, I'd really appreciate any help.