My Airport Extreme is set up in DHCP + NAT mode. It is distributing IP addresses on my LAN in the 10.0.x.x range. It is connected to the internet via an ADSL modem. This modem performs the necessary NAT functions for the networks to connect.
The AirPort is providing NAT service...and....you say that the modem provides NAT service as well. What you have described is a network error known as Double NAT, since you only want one device on a network providing NAT service.
You can often get away with Double NAT on a simple home network, but it is best to avoid the error if possible.
Soon I'm changing to a different ISP and will connect to the internet via cable. The modem/router that will be provided is distributing IP addresses in the 192.168.x.x. range. This modem is hardly configurable, e.g. the distributed IP address range cannot be changed.
Now things will be even more complicated. The AirPort Extreme is providing DHCP and NAT. So too, will the modem router be providing DHCP and NAT. In addition to a Double NAT condition, you will have two devices both providing DHCP services. In effect, you will have two devices both trying to perform routing services on a network. You only want one device to provide routing services on a network.
It is possible to put this modem/router in Bridge Mode.
I would like to keep my LAN set up in the 10.0.x.x IP address range. My solution would be to put the new modem/router in Bridge Mode and let the Airport Extreme provide the necessary NAT.
Good plan, if "bridge mode" on the modem/router will really convert the device to act as a simple modem. That would be something that you need to find out from your ISP or the modem/router manufacturer.
In "bridge mode", DHCP and NAT are turned off.
Things would be much simpler and much better if your ISP could simply provide you with a simple modem....Not a modem/router.
Does anyone know how to set up the NAT portion of an Airport Extreme for this particular situation?
If the AirPort Extreme is doing DHCP and NAT as you state, then you are all set. No adjustments will be needed.
The Airport Extreme will be connected to the WAN side via an IP address in the 192.168.x.x range
No, this is not correct. A 192.168.x.x address is a "private" LAN side IP address. When you configure the modem/router correctly in bridge mode to act as a simple modem, the WAN port on the AirPort Extreme will receive a "public" IP address, which is what you want.
Remember, in "bridge mode", DHCP and NAT are turned off, so your "modem/router" will not be providing DHCP or NAT services at all.
The public IP address is dynamic....unless your ISP provides you with a "static" IP address. The public IP address could be virtually anything.....but it will never be 192.168.x.x or 10.0.x.x
while the DHCP part of the Airport Extreme needs to distribute IP addresses to the LAN in the 10.0.x.x. range.
Since you have the AirPort Extreme configured to provide DHCP and NAT, and the default setting for the AirPort is to use the 10.0.x.x range, devices on your "private" network will always receive an IP address in the 10.0.x.x range.