In Airport Admin Utility, check that your Airport Base station is set to Bridge mode. Bridge mode essentially makes the Airport act as an imaginary cable to your router. It's possible your Airport is currently acting as a second router, distributing a new set of IP addresses (typically something like 10.0.1.1).
Once you are sure you are getting your IP number from the modem and not the Airport, connect to your modem/router's web administration page (typically something like
http://192.168.1.1 or
http://192.168.1.254 - you can find the actual address in System Preferences > Network > Airport > TCP/IP -- it is the address after the word "Router").
Once you're logged into the modem's website you should be able to find a port forwarding page, or Firewall NAT page, etc - look around until you find it. Then all you have to do is enter your machine's IP address (found in System Prefs) and the port that you want to forward.
It might be an idea to Google the modem (what model is it anyway?) and check that it supports port forwarding before anything else.
Good luck - let us know how you go.
edit: attached a picture of my router's setup so you can see how easy the last step is.