android does alot of synchronizing and checking in the background that will use you data (internet) for things like gmail and calender there ways to reduce/stop it from doing this

to start of with go somwhere with free wifi and setup the google account stuff that will sync everything for the first time which is what the phone may be trying to do now, more importantly once synced once you can go into the options and tell it not too sync automatically which is great

secondly get the app apn droid this can disable you 3g when not in use by simply hitting a button which will stop anything from using the internet, however it does stop you using 3g telephony but if you need it you use switch it on while in use then off again, the better use for this app is it stops games with adds or accidentally opening the internet from draining your credit

there are other ways to block internet access to specific apps but this requires the phone to be rooted so you have admin access and is not easy/recommended unless you no what your doing

 

it happend to me you have to (turn off mobile networks) in the options menu

 

I suggest you get a data plan so you can use the phone to it's full potential

 

I've had the same problem, I'm on Orange payasyougo, and I had topped up