I did this for our network not a while ago and it works. We are connected via ADSL and we accidentally bought a Cable router instead of a new ADSL one. I had the idea of bridging the routers so I could connect to one network and the others are connected to the other, and it worked. We have a Belkin N150 ADSL Router connected to our network, and a NETGEAR N+ Cable router connected to the ADSL router. Although there isn't any quality increase from the NETGEAR (it ahs to be connected to the initial network ground instead of connected to a lower quality router) the quality is good, but not good for me (although I have a wireless N+ adapter

).
So basically, just wire the router up to your current one if it's Cable, otherwise if you're initial network is cable and you have the 2nd router as ADSL, there's not really any way of doing that. So if you have a Cable router to the ADSL router, get and Ethernet cable and wire the Ethernet user from the ADSL port to the Internet port on the Cable router

.
-SSG