|The second router will have to be connected and setup properly.|
First, go into your router and find the DHCP scope and it's IP address and make note of them. Generally speaking, the scope on most SOHO routers is something like the following:
192.168.0.100 to 192.168.0.199
Continuing with the above example, your router's IP will most likely be 192.168.0.1
Now, using a crossover cable, connect from a LAN port on your router to a LAN port on the other router and configure the LAN IP address of the second router to be within the same subnet, but outside the DHCP scope on your router.
Following the above example, the TCP/IP settings for the LAN side of the second router should look something like the following:
Subnet Mask: 255.255.255.0
Now configure a DHCP scope on the other router something like:
192.168.0.50 to 192.168.0.99
This way your scopes are separate, each router has a unique IP and everybody connected, and the routers themselves, should all be communicating, and accessing the internet properly.