How can I move my router to a different room in my house?

How can I move my router to a different room in my house?

 

I used to have Uverse TV and internet, but now I only have the Internet. I want to move my router from my office upstairs to my living room downstairs so I can plug my ps3 and Roku HD-XR Player up to the router directly. I tried just moving the router and plugging int he coax that was hooked up to the main tv box, but it didn't work. I would love to rewire myself if possible without have to pay at&t to come out and do it.