Okay, so the problem you're having is likely due to your Airport Extreme ignoring stuff (as a security measure) that Xbox Live is sending the Xbox. While there are a few ways to deal with this, I've generally found the easiest is to ensure your Xbox is given the same IP address by the AE every time it connects, and to set the AE to then not block anything sent to that IP address.
First we need to get the Xbox's wireless MAC address, which you can find on your Xbox by going to Settings, System Settings, Network Settings, selecting your wireless network from the ones that appear, Configure Network, Additional Settings (push the left thumbstick to the right), and finally Advanced Settings, then the MAC address should be displayed.
Just to be clear, a MAC address has nothing to do with Apple's computers. It actually stands for Media Access Control and is a quasi-unique code that nearly every network adapter has. We're using it here so your Airport Extreme can easily recognise the Xbox.
Now you've got the MAC address for the Xbox, open AirPort Utility, select your Airport Extreme and click Edit, then the Network tab. Click the plus button under the DHCP Reservations box, type Xbox 360 (or whatever you want) as the description, type the Xbox's MAC address into the MAC Address box, then click the IPv4 box, change the last number after the . from 2 to 35, and click Save.
Now we have the Xbox getting the same IP from the AE every time, we need to tell to stop filtering stuff that's sent to that IP.
On the same Network tab in Airport Utility as before, click the Network Options button, tick "Enable default host at:" and enter 35 as the last two digits (so it matches up with the full IP address in the IPv4 box earlier). Finally, click Update, and when your Airport Extreme has finished restarting, try the connection test on the Xbox again and (hopefully) bask in the glow of a nice open NAT setting.