I know this is an old thread, but I landed here from Google with the same problem, so I'm hoping this will help someone:
I got an unlocked HTC One and signed up for T-Mobile. I could make calls, but Internet browsing didn't work. Under the settings for mobile data, it said it was unavailable.
It turned out to be because I didn't have an "APN" set up for T-Mobile. I clicked on the mobile data option which took me to another screen where I clicked on "Access Points" (I think). And there I could manually enter a new APN entry. I found a T-Mobile support page (sorry, the forum won't let me post the link - but you can probably find it via Google) which had APN settings. After that, I could surf the web! Hopefully your carrier provides APN settings somewhere, or you can try contacting their Support.