Dou itashimashite and iie are both right.　　By saying どういたしまして, you are accepting that you did something kind for that person. Be careful because this can sometimes sound arrogant. いいえ, is used exactly as Michael said it, "Oh, it was nothing," or, "No problem."

You don't really say "you're welcome." Instead, いいえ　（iie), is used. It has the feeling of "oh it was nothing."

どう致しまして (Dōitashimashite) = you're welcome / don't mention it

A) Arigatou Gozaimasu! Respond with... B) Dou Itashimashite! (You are welcome!)

KIKILOLO