Nope, you shouldn't get charged for using a router. Your ISP may not want to give you phone support while you are using one though. Here is a diagram and info showing you what to do for a router setup, it is pretty easy:
http://www.xbox.com/en-US/live/connect/router.htm
I recommend the Linksys WRT54G - very common router you can find everywhere, it is pretty cheap, and supports wired and wireless connections.
http://www.xbox.com/en-US/live/connect/router.htm
I recommend the Linksys WRT54G - very common router you can find everywhere, it is pretty cheap, and supports wired and wireless connections.