How to say 'how do you do' in Japanese

When you meet a person for the first time, you can say はじめまして or in romaji 'Hajimemashite'which means 'How do you do?'

Then you can say どぞ　よろしく or 'Dozo yoroshiku' in romaji. It actually means 'Please be nice to me' and is the equivalent of 'Pleased to meet you' in English.

For example, after being introduced to Mr Tanaka, you can saｙ
たなかさんで　はじめまして　どぞ　よろしく　(Tanaka-san, Hajimemashite, dozo yoroshiku.)
Mr Tanaka, how do you do? Pleased to meet you.