Android phones
Go to Settings and select the option Data usage. From here simply turn slider across the Mobile data switch from on to off. Alternatively, most Android smartphones will let you quickly turn on/off by sliding your finger down from the top of the screen and then simply deselecting the Data icon. Another option is go to Settings>More>Cellular Networks and turn off “Data Enabled”.
Apple iPhone
On iOS 8, go to Settings> Cellular> Turn the option for Cellular Data to Off.
Windows Phone
On Windows Phone 8, Swipe left and bring up the alphabetical list of Apps > go to Settings > turn data connection off.
Blackberry
Pull your finger down from the top of the screen and open Settings. You then need to open Network Connections and Mobile Network, switch Data from on to off.