From a post by JohnWill:
Connecting two SOHO broadband routers together.
Configure the IP address of the secondary router to be in the same subnet as the primary router, but out of the range of the DHCP server in the primary router. For instance DHCP server addresses 192.168.0.2 through 192.168.0.100, I'd assign the secondary router 192.168.0.254 as it's IP address.
Disable the DHCP server in the secondary router.
Connect from the primary router's LAN port to one of the LAN ports on the secondary router. If there is no uplink port and neither of the routers have auto-sensing ports, use a cross-over cable. Leave the WAN port unconnected!
In your case connect the secondary router to one of the ports on the switch. If the router has 1 WAN and 4 LAN ports, you will change one switch port into 3 ports on the router. So you will only gain 2 additional connections; Your 4 port switch has 1 port going to the router, leaving 3 for your PCs. Adding the 2nd router will use one of those ports, leaving 2, and adding 3, so you will go from 3 ports to 5.
You need to turn off DHCP in the 2nd router, or the two routers will both be trying to assign addresses to your PCs, which is not good.
Switches can be interconnected with no configuration, just need one with an uplink/auto-sensing port, or a crossover cable. One port on each switch is used for the connection, so connecting a 4 port switch will still only give you 5 ports total, 2 on the original switch plus 3 on the new 4 port switch.
If your router has additional ports, you can run another long wire to hook to another switch (or to the LAN port of the 2nd router); then you would have 3 ports on each device.
It is possible to connect the WAN port to the switch, so all 4 LAN ports on the 2nd router will be available, but this will add a second NAT layer to your network, meaning the PCs connected to the 2nd router won't be able to share files/printers with the PCs on the switch, and vice versa, at least not without a lot of configuration that most cheap routers won't support anyways. Not worth the hassle for one extra port considering how cheap switches are now-a-days. You can find good 16 port switches for around $35-$40
HTH
Jerry