This is easily set up with the latest AirPort Utility software. When the second AirPort base station is powered on, it will become available in the "Other Wi-Fi Devices" list, at the upper left. Add that unit, then go into its Wireless tab, and there select "Extend a wireless network" from the Wireless Mode menu. The second base station then extends the range of your wireless network. In AirPort Utility, the arrangement looks like this.
About usage and performance: The best way to use this extended network is to connect the equipment near the second base station by means of ethernet cabling. This is optimal networking, particularly among devices connected directly to that remote base station. If you have to use devices wirelessly with that remote base station, you will experience throughput roughly cut in half, because it involves conducting a wireless session with that remote station, and that remote station then has to convey the data in a wireless session with the primary base station.
Begin by setting up the cabling. Connect the Macs and devices to the device connections in the back of the base station. Leave the WAN connection empty, as you have no Internet opportunity with this arrangement.
Now plug in the base station and turn on one of the Macs.
Launch the AirPort Utility.
In the modern version of the utility, your base station will appear pictorially,
in the bottom of the frame.
At this point, you should expect the base station to be have a blinking amber
light, indicating that configuration adjustment is needed.
In the AirPort Utility frame, you should see a badge with a number in it,
indicating the number of issues, and enumerated issues to the right.
Go into Edit on the base station.
Click on the Internet tab. Change the settings to have:
Connect Using: Static
Router Address: __(empty)__
DNS Servers: __(empty)__
Now click on the Wireless tab.
If you have another base station providing wireless, here you would want
setting:
Networking Mode: Off
Now click on the Network tab. Here you want setting:
Router Mode: DHCP and NAT
Optionally change the address range from 10.x.x.x to 192.168.x.x if you have
another base station providing wireless in the default range of 10.x.x.x, to
prevent any confusion.
Restart your base station to put the changes into effect. This brings you back to the main, pictorial frame. The base station light will be blinking amber, still, because there is no Internet connection. The AirPort Utility will show complaint: Ethernet Unplugged. At this point you can click on the amber circle relating to the absence of an Internet connection and choose Ignore, to tell the base station to ignore that, as it will never get such a connection. The light will turn to steady green. You are all set.