Re-installing OS X with apartment Wi-Fi I need to re-install OS X Lion and I'm at a stage where when I turn my laptop on, it needs an internet connection to proceed.

I have a good strong Wi-Fi signal, but I need to sign in. I usually do this by opening Safari, which prompts me with the sign-in page. I can't open Safari though because I'm in the re-install screen.

Any ideas on how to get around this?

Also, what's the proper terminology used here?
First I'd try to just connect to the Wi-Fi network and then run the recovery. But this will not work if you have a new and empty hard drive (i.e. no OS X  recovery partition on the hard drive) and need a full Internet Recovery from Apple's server.

If it doesn't work, I'd try and connect the Mac to another Mac or a Windows PC using a common Ethernet cable (network cable) and enable "Internet Sharing" on that system. On a Mac, Internet Sharing is simply enabled via System Preferences > Sharing. I don't know how this is done in Windows.

If that doesn't work either, I'd simply see that I connect the Mac to a different Wifi or ethernet-based network that doesn't require you to go through such a captive portal. Just remember not to enter any account credentials over public Wi-Fi (such as your Apple ID).