How to expand the number of ports on a router ?

Most broadband routers on the market today are really a combination of a router and an Ethernet switch with multiple LAN ports.

The WAN port is used for the Internet connection. The built-in switch is on the LAN side of the router, where clients connect.

Because a broadband router/switch conceptually expands a single port on a modem to serve several client PCs connected to it, there may be a tendancy to think that another router is the way to expand the network further - that is NOT the case.
Ports on the LAN side of the router are in essence a switch. Ethernet switches are usually expanded by adding more Ethernet switches.

An Ethernet switch is the best way to add more ports to a broadband router. An Ethernet hub can be used as well, even though it is not an optimal solution for larger LANs (hubs broadcast packets to all clients and introduce congestion in larger LANs).

Most modern routers and switches have auto-crossover ports, meaning you can connect a regular (straight through) Cat5 cable between any LAN port on the router and any port on your switch. If your switch has an "uplink" port, use it for the connection to the NAT router. If you use older router and switch, where both devices have no auto-crossover or uplink ports, you may have to use a crossover cable between the router and the switch.

Note: Routers can sometimes be used to expand the number of LAN ports, however introducing more than one NAT router in the same network is not a good practice. It presents many configuration issues (and frustration) that are beyond the scope of this article). If you have to do it, only use the LAN ports on the second router and disable it's DHCP server.