There was a time when only Americans would say, "You are welcome" and British people would only say "Not at all" or "Don't mention it". American culture has now become so dominant in the world that learners like you are surprised to hear "Not at all".

To expand on Su.Ki.'s answer, you might also hear "No problem" used in the same way as "Not at all".

'Not at all' is more or less the equivalent of 'de nada' (or similar expressions) in Latin languages, with the suggestion that the favour was an insignificant one, or no trouble. So, if you think that it's appropriate to the situation to suggest this, then 'not at all' is fine as a response. Otherwise, use 'You're welcome'.