How do you set up a router without it being plugged into your computer?

We are getting high speed internet soon and it comes with a free router, I have a laptop my brother has a xbox 360, we both want to be wireless. I don't want a router plugged into my computer because I want the freedom to go other places in my house with it, wireless. I have read some stuff online, some people say you do need it plugged into a computer other people say you don't. I just want a soild answer, do I or don't I? And if I don't, how would I set it up.