When you're connected. There should be an SSID on the top of your home screen visible. That is the name of the provider or router. for example, If you were at Mcdonald's that provides free wifi. It may say Mcdonald's on the top of your home screen or something to that effect.
The wifi will be on your screen when you turn it on. To be connected you need to check manage connections and it will show you. Some themes do not show the ssid so that isn't foolproof
Under some conditions (which I haven't yet discovered) the WiFi icon on the MAIN screen will show grayed-out like it isn't active, but if you press the menu button, it shows bright. Then pressing the escape key to go back to the main screen aqain shows it grayed-out, etc. In this situation, I AM connected and using wifi -- if I go into to the browser, for example, if shows using the wifi.
Seems to be a bug of some sort in the theme? (I'm using the default Verizon theme on the Bold 9650)
--UPDATE--
I have found that if I do a simple power-off, then back on, the icon displays correctly (bright)