Changing the subnet of the other router would only be necessary if both routers were to serve as DHCP servers. You would still need to change the IP of the second router. For example if one is 192.168.1.1, the other should be something like 192.168.1.2
If you're going to use it as a switch, simply plug a standard CAT5 cable into a LAN port on the second router and make sure DHCP is disabled ont he second router.