For your network, you need a modem to connect the outside world (your phone line) to your PC and allow you to use broadband.
You already have one of these as you're using broadband.
A router is something which can connect multiple machines together, and then route them on to another destination.
You can buy a combined modem/router which is basically a single box with lots of ports in it, for you to connect multiple PCs into and they all share the internet connection through the modem.
If your modem has the appropriate ports to connect a router to it (usually via an ethernet (aka Network) cable) then there's no reason why the router won't accept the wireless connection and route it through the modem and out to t'intarweb.
You might want to check that you haven't got something silly (ie, cheap!) like a USB modem as you probably won't be able to connect the wireless router to it.
This article explains it all in Microsoft jargon with pretty pictures:
http://www.microsoft.com/athome/more...lesssetup.mspx