Connecting to Wifi

I have only tried to connect to Wifi a handful of times. At my house I use an open internet connection and according to the phone the signal is weak so i understand that. recently i was in a fast food restaurant with free wifi and the signal was excelent and it still said it could not connect. When i try to connect i go to the connections screen - set up wifi - then scan - it tries to connect. it somtimes says its connected but the icon below the signal is not lit up.
Thoughts?