Well, I finally found the answer here:
http://forums.practicallynetworked.c...ead.php?t=6117
In short, you disable the DHCP of the downstream router (the second one) and give it an IP address outside of the DHCP range of the main router (the first one--IP address was 192.168.1.20 in my case). For the connection, you can use normal network cabling, but it has to go from LAN port to LAN port, rather than LAN to WAN/uplink. I now have both routers working perfectly, both wired and wireless. It's a beautiful thing!
Thanks to everyone for the helpful suggestions here.