I'm not an expert about all the flavours of wifi, but just to be sure: is it a particular wifi security mechanism or you mean that whenever you access this wifi with you computer, the browser shows you a form with user and password fields?
If that's the case, that's called captive portal. There is no common recipe for making the yun work with such portals (everyone is different). You need to mimic your browser behaviour, for example making a sketch that invokes curl with method POST and fields user/password