Connecting the pieces

Clean start:

iptables -F INPUT
iptables -F OUTPUT
iptables -F FORWARD
iptables -F -t nat

Transmit all packets:

iptables  -P INPUT ACCEPT
iptables  -P OUTPUT ACCEPT
iptables  -P FORWARD ACCEPT

Masquerade private addresses:

iptables -t nat -A POSTROUTING -o eth0 -s 192.168.1.0/24 -j SNAT --to-source 1.2.3.4
( or iptables -t nat -A POSTROUTING -o eth0 -s 192.168.1.0/24 -j MASQUERADE )