The first thing to check is you have the correct APN settings. Goto settings > Wireless and network > Mobile networks and then make sure Use packet data is ticked. Then tap Network mode and select GSM/WCDMA(auto mode).
Now just to check, tap Access Point names and see if your providers settings are there. If not, contact your network provider and they will send you the settings.
For future reference, to turn mobile data off and on long press the power key and tap Data network mode. This will disable data mode and re-enable it when needed.
Cheers.
Ray