It's simple really - if the phone has an internet connection via wifi, it'll use wifi - otherwise it will use the 3g data connection.

If you don't want the 3g data to be used you can either make sure there are no programs running that download data or turn the phone on airplane mode to disable everything (including voice).

Internet Access. I recently bought this phone and am very pleased with it but there's one issue which is driving me nuts and Samsung's support staff can't even understand the problem let alone give me an answer. It's all about Internet access.
The phone happily connects to my house WiFi router which provides me with two ways of accessing the Internet from the phone one of which is free and the other isn't. The question is "How do I tell how my Internet connection is routed?"
There's an obscure setting in the advanced section of the phone WiFi setup called "WiFi sleep policy" which has the options "When screen turns off", "Never when plugged in" and "Never" . This isn't very clear and when I selected "Never" and turned off my house router I expected the Internet access to stop but it didn't. It might be that the device is so clever it automatically flips to the cellular network route if the WiFi connection goes down but I wish it wouldn't because that could run up a large bill without me realizing it. Can any of you geniuses elaborate on this issue please?