How can you use your own router?

Hey everyone,

So I've just been wondering about Apple's Routers, the Airports, and I don't understand how I could use one. All internet providers I've come across so far have given me their own little box with their logo on it that you plug your phone line into directly.

Now I'm not a router geek, but as far as I know, you can't plug a phone line directly into a router, you first need to have a modem, that will transform that into an Ethernet plug, which then goes into the Router, which then broadcasts your WiFi or passes on the connection via Ethernet.

So if I were now going to take the router that's downstairs that O2 provided me with and remove it, I would simply not be able to plug in an Airport base station were I to buy one.

Does this mean I would also have to buy a modem, separately? But then how the hell am I supposed to know how to configure a modem? As far as I know, you can't access what's inside a modem with an IP address like you do with a router.

Also, my router's locked down with a password so that I can't access any of the settings. O2 does this for me, and I can't change anything, also, I can't even know what the settings are so that I could replicate them (username, password) on my Airport or other new router.

... Or could I just plug in the Airport base station into one of the Ethernet outlets of the existing O2 router? But wouldn't it be stupid to use two routers? The point here is that my O2 router is very unstable and reboots randomly during the day. It's a manufacturing defect that affects almost every O2 router and it's "normal", so they won't replace it.

Thanks for your help!