On Windows Phone 8 it's relatively easy, touch the "settings" icon;
Then scroll down until you see "mobile network" and touch that;
The second option, after your mobile network, is titled "Data Connection" and is typically set to "on".
Beneath that is a "Data roaming options" drop down that can either be set to "roam" or "don't roam";
If you change the option then the explanation text beneath it changes;
(roam) - "Depending on your service agreement, you may incur extra changes when using data roaming"
(don't roam) - "When entering a roaming area, your data connection will be turned off"
If you don't want roaming charges to appear on your bill (for data) then select "don't roam" in the drop down. This takes effect immediately.