A bit more understanding of NAT router operation will clarify what's going on and guide you toward making the required router configuration changes needed to create more complex networks.

What is a Router ?
Stated as clearly as possible: A router is a device used to interconnect separate networks of computers. The individual destination addresses of packets of data arriving at the router are examined and compared to the address ranges of the networks to which the router is connected. If a packet of data is addressed to a machine on another network, the router will briefly assume responsibility for that packet by "routing it" (re-transmitting it) out of the appropriate network connection interface.

 Packets arriving at the router's LAN interface with a destination IP falling outside of the LAN's address range are "routed" out of the router's WAN interface.

What is DHCP ?
D.H.C.P. stands for Dynamic Host Configuration Protocol. It is a very slick means by which any computer wanting to participate on a local area network can be automatically assigned an available (not currently in use) IP address and provided with all other important local area network information, such as the IP address of the LAN's gateway interface.

When a computer's network interface has been configured to "obtain its IP address automatically", it sends a "broadcast" throughout the local LAN using a special Ethernet broadcast address which it can use without knowing anything else about the local network's configuration. A listening DHCP server — in this case running and waiting patiently in our NAT router — answers these crys for help by replying with all the specific LAN settings each computer needs to communicate locally and globally. In this fashion, the configuration of individual machines is handled automatically.

NAT Routers are usually also DHCP clients too.
As we've seen, NAT routers contain a DHCP server that is used to automatically configure their client computers on the LAN. But many NAT routers are also DHCP clients of the public Internet ISP.

When the NAT router is powered up, it broadcasts its own DHCP query out of its WAN-side network interface asking the Internet ISP to assign it an available public Internet IP address and to provide it with any other information it will need for communicating over the ISP's network.

In terms of your own NAT router configuration, this means that whatever you do, you will want to be certain that your NAT router(s) translate their public WAN-side IP into LAN sub-networks that fall completely within these private IP ranges. This also means that you are free to use any of the IP address ranges shown above which your NAT router's configuration options will allow.

Putting it all together . . .
We can distill all of the information above into three simple rules:

 Unless your ISP requires non-DHCP configuration for your primary external NAT router, or you have special needs for establishing fixed addresses for specific machines within your network, you may use your NAT router's built-in DHCP server and client to automatically assign and establish all IP addresses within your network.

 Every NAT router must be configured to use blocks of non-public, private IP addresses shown in the table above.

 Routers decide whether to route local data packets "upstream", out of their WAN port based upon whether or not the packet's destination IP address falls within the local LAN address range. Therefore, the IP address assigned to a router's WAN port must lie outside the address range the router is using for its LAN-side addresses.

Following these two simple rules, a typical two-router configuration could be setup with the external NAT router configured to issue LAN addresses in the 192.168.1.* range and the internal router configured to issue its LAN addresses from the non-overlapping range 192.168.2.*.

Since the internal router's DHCP client would receive an address for its WAN port from the external router's LAN range (192.168.1.*), no address it receives — where the third address byte is "1" — could possibly conflict with any of the 192.168.2.* addresses it will be assigning to its own machines. Therefore the internal router will always be able to determine whether data packets are bound for other machines within its LAN, or need to be "routed" out of its WAN port.

If your routers allow the third number of their LAN networks to be user-specified and configured (as all routers we've seen do), while assigning the final address byte automatically as needed, you can sequentially and uniquely number every NAT router within your network (of any complexity), and use that number as the third address byte assigned to machines within that router's LAN network. In this way, EVERY computer will have a unique private address, none of the private LAN networks will be overlapping, and there will never be any collision with the Internet's public IP space.

Making the electrical connection
Standard Ethernet network cables with standard "RJ-45" Male connectors are wired "straight through". This means that pin 1 at one end is wired to pin 1 at the other end, pin 2 connects to pin 2, and so on for all eight pins. This means that pins which connect to signal outputs at one end of the cable need to connect to signal inputs at the other. This is handled automatically for users by having their RJ-45 Female counterparts available in two different signal arrangements:

PC Ethernet adapters uniformly use one set of pins for inputs and outputs (we'll call it "A-style"), and Ethernet switches and hubs deliberately use the reverse arrangement ("B-style"). This allows PC adapters (A) to be plugged directly into switches and hubs (B) with "straight through" cables.