Welcome.
If you're having trouble getting internet connectivity in a specific app, such as a web browser, you may want to try a different app.
If you have no connectivity at all then you will be unable to register your phone, get apps, etc. Try it on wifi. If it works on wifi, check to make sure you don't simply have mobile data turned off.
Settings -> Wireless & Networks -> More... -> Mobile Networks -> Data enabled
Also look there for other settings that might affect it. If a setting isn't at fault and rebooting the phone doesn't help, you may need to contact your carrier.