As Saad said, the DCHP/IP Address allocation is the thing to sort. I recently added a wireless router to my already happily running non-wireless network. The approach I found best was to setup the wireless router to not act as a DCHP server first before connecting it to the non-wireless router. That will allow your original router to continue working as before and the wireless router to simply act as a hub. As for connecting them together I just used the same cable that I orignally had between my laptop and the non-wireless router.
Regards
Stoney