You can never surf the web over the cellular network without your operator charging you.

I know only my country's operators' tariffs, but I just can't imagine anyone giving free data transfer to users in their network.

The usual pattern:
No dataplan = you surf with a lower speed than with a package, and you are probably being charged by transferred kilobyte. Usually expensive with even light use.

Dataplan = a quota to transfer, usually with a higher speed and a fixed free every month, unless you go over that quota of course.