Then you'll need to configure iptables to forward the packets from your internal network, on /dev/eth1, to your external network on /dev/eth0. You do this will the following commands:
echo 1 > /proc/sys/net/ipv4/ip_forward
You should now be NATing. You can test this by pinging an external address from one of your internal hosts. The last step is to ensure that this setup survives over a reboot. Obviously you should only do these last two steps if your test is a success.
/sbin/iptables -t nat -A POSTROUTING -o eth0 -j MASQUERADE /sbin/iptables -A FORWARD -i eth0 -o eth1 -m state --state RELATED,ESTABLISHED -j ACCEPT /sbin/iptables -A FORWARD -i eth1 -o eth0 -j ACCEPT