Not used it at an airport yet, but have in other places - bars, etc.
All systems seem to be based on you either having a roaming account with a provider (or group of providers), usually tied to your mobile phone account. If not, just try and select a web page, and you will get directed to a "bill me now via my credit card" page - fill in the details and off you go.
Similar to the wired setup in many hotels now.
Word of warning - make sure you have an adequate firewall installed before using any high speed internet connection from your own PC - whether this is at home, in a hotel, or one of these wireless hot spots. I have regularly detected other computers trying to "break in".