How does the Airport work when the wired connection requires a webpage login to be activated?
You can set it up as a bridge, so that it will take that page and just send it wirelessly to your browser so you can log in or give your credit card, or click on the terms, whatever you need to do.
From one post on the apple boards
The AirPort Express needs to be configured in Bridge Mode to work on most hotel networks. If you already have the Express setup to create a wireless network, you can check the Connection Sharing setting quickly as follows:
AirPort Utility - Manual Setup
Click the Internet icon
Connection Sharing = Off (Bridge Mode)
When you get to the hotel, connect the ethernet cable to wall jack, power up the AirPort Express and open the browser on your computer. The hotel's log in page will appear to so you can agree to terms and pay the fees, etc.