I think the point of the question was they are going over their home broadband allowance since getting the iPhone.
the phone will only use the internet if you have something enabled on it that uses the internet, have you got it set to check your email every few minutes? if so you might want to turn down the frequency of the check. (not that checking emails should use much)
You could turn of all other devices that use your router (it's a router not a modem) and then watch the lights on it with just the iPhone connected, if the lights are flashing a lot then something you've got on the phone is using the internet.