How to share a WiFi hotspot using AE?

I have the following hardware, which I had set up successfully at my previous premises for all devices to share the ADSL+ service.

* Apple Extreme Base Station (802.11N 3rd generation)

* Cisco LinkSys WRT150N Wireless router

* Ethernet cables

* Windows XP laptop, iPad, iPhone, MacBook

However, at my new apartment, the only internet access is via a WiFi hotspot-style service supplied by the apartment building owner. The WiFi service has no authentication - security is via a username/login screen when you try to access it. The problem is that only one device can connect to it at any one time.

I haven't had any luck trying to get this setup to share the WiFi service with my various devices. I note that this article (http://support.apple.com/kb/TA21385) says that it can be done (using only the Airport Extreme), but doesn't tell you how to do it. Can anyone help?