I found this surprisingly difficult; though it turns out the steps involved are quite easy...once you know how.
For this article I'll assume your existing LAN is 10.0.0.0/8 with 10.0.0.1 as the default gateway. I'm going to give the wireless LAN router 10.1.2.3. Substitute 10.0.0.1 and 10.1.2.3 below for something suitable for your LAN (and change the 255.0.0.0 network mask accordingly).
These instructions assume factory reset status, with the "router" switch (on the case) set to "On", rather than "Off" or "Auto". The AirStation is connected to the LAN hub using the Internet socket (the blue one).
1. Connect a computer to the Air Station directly (with ethernet cable, to one of the four LAN sockets), and set your computer to use DHCP, so that it gets an IP address that can see the Air Station! (Most likely your computer will receive 192.168.11.2.)
Note: The computer you connect with does not need to have a wireless card in it; it does have to have wired ethernet though.
Tip: Don't use your main computer for this step; that way you will be able to still use your main computer for: a) googling when you hit problems; b) ping tests (see step 5 below).
2. Connect by browser to 192.168.11.1
Use root as the username, with blank password.
3. Internet/LAN | Internet
IP Manual: 10.1.2.3
Default GW: 10.0.0.1
DNS: (whatever DNS server you use: this is what will be handed out to wireless clients that connect using DHCP)
4. Wait for it to restart. (I also enabled pings at this point too.)
5. Then cycle the power; this appears to be essential.
Now you should be able to ping 10.1.2.3 from outside, and also ping from the connected computer to 10.0.0.1. And if you can do that then you can also connect to internet! You are done, time for a nice cuppa.
6. Test from a wireless device to make sure you are required to type in the key.
7. Set a root password.