You need to make sure you have data traffic turned off. From settings select Wireless & Networks>Mobile Networks and then untick Data Traffic.
Wifi doesn't incur any costs so if you want to use your phone for browsing/Facebook updates/downloading apps from the market etc then use wifi when available.
You can put a widget on your homescreens called Data Traffic to switch it on and off if you do have a small amound of net access, but if your package doesn't include this you will be paying a standard daily rate with your carrier and its probably one of your apps connecting and updating that is causing the cost to your account.
