Hey! That's what we're here for!
Just to clarify that for you, the Airport Extreme Basestation simply acts as a router for broadband, meaning multiple computers behind it (on your LAN) are seen by the internet (WAN) as ONE computer - just the basestation. This is called NAT (Network Address Translation). The basestation, depending on the model, does have a dial-up modem built-in for using your phone line to connect to your ISP (Internet Service Provider), if dial-up is what you pay for, but it does NOT have a high-speed modem for one good reason: There are many different types of high-speed.
If you have high-speed through cable, your coax cable connects to it's appropriate modem, which then connects to your basestation's WAN port. If you have ADSL high-speed, the special phone thingy connects to it's modem, which in turn connects to the basestation... etc.
The high-speed modem they gave you is also a router? If that's true, you may want to look into turning off any routing capabilities it has and use it only as a modem - let your basestation act as the router for you. This will simplify more advanced networking tasks you may be interested in, for the future.
Let me explain. (By the way, I am a networking specialist for the feds - <wink>) Networking traffic (packets of data) go through ports. Firewalls, very simply, close those ports. Some games require you to open ports to play them online. If you are using NAT, (which you are because you have more than one PC behind the basestation sharing the connection) you will need to forward any traffic on (for example) port 41000 to the computer used to play that game. This means that any internet traffic coming into your LAN from the WAN on this port will be forwarded to the proper computer instead of being blocked.
Different apps/games use different ports (ftp, for transferring files, uses port 21, etc). So, if both your modem and basestation are blocking ports, and your "Super Turbo Turkey Puncher 3" requires port 41000 to be open, you would have to open 41000 on both. If you disable the routing on the modem, you only have to open it on the basestation.
I realize it sounds like more security, but in reality, NAT is no substitute for a real firewall. Hackers can get around NAT fairly easily, but NAT acts close enough like a firewall for the money-grubbing companies to be allowed to say (to fool networking newbies) that their broadband modems have firewalls built-in. That being said, two routers will just cause a headache. (Literally - this will confuse you but it's true - you'd have to forward the traffic from the modem/router to the basestation, then you'd have to forward it from the basestation to the computer).
(wow, this is almost a book! It might be clearer if ya read it twice! lol) Anyway, cheers, and enjoy your new setup! Let me know if you have any questions.