There can be subtle differences from carrier to carrier, but it's almost always true that calls and plain text messages don't use data. It's also true as someone said above that some apps installed on a smart phone will use data in the background without your knowledge. To protect against that on an Android phone you can turn off data. As described here:
How to Limit Data Usage on Android - Tech Advisor
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How to completely turn off your data connection
Swipe down from the top of the screen, select Settings, press Data usage and then flick the Mobile data switch from On to Off - this will completely turn off your mobile data connection.
Note: you will still be able to connect to the internet and use apps as normal if you are connected to a Wi-Fi network.