Hi
If you want to connect a wireless router to an existing router, you need to set the second router as an access point. This way it will act as a hub but will allow you to pass IPs from the DHCP of the first router. If you can't set the second router in access point mode then you won't be able to do this unless the two routers are the same model, then you may be able to bridge the two, but that creates a whole new set of issues.
Best thing to do is go into the router interface(open a browser and type the IP of the router) in the setup pages you should find a place to set the router as a Gateway, or as an Access Point. If you don't see those options then you won't be able to use it this way. You may also need to turn off DHCP on the second router(it usually does this automatically when set to access point.
Trevor