はじめまして
hajimemashite!
= Nice to meet you!

はじめまして。どうぞよろしくお願いします。 (polite)
= はじめまして。どうぞよろしくおねがいします。
= Hajimemashite douzo yoroshiku onegai shimasu.
= Nice to meet you! (No translation. Something like Thank you in advance/please be kind to me.)

~Said upon the very first introduction to someone, it's a set phrase to be polite
http://i.imgur.com/fqMLeiT.png