Router configuration

Working on a small network, we want to set up a WiFi hotspot that will use our current Internet access. We have one router/firewall/dhcp server immediately after the modem that serves the network. We want to install a second router that will allow internet access but keep the people in the hotspot from seeing the rest of the network. I know we have to change the dhcp service and subnet mask on the second router, but when I tried it earlier this week I ended up with two dhcp servers on the same network - it was not pretty! Any help appreciated. Thanks.