This phrase is used when you first meet someone or when you ask someone to do something. The polite way to say this is "YOROSHIKU ONEGAI SHIMASU."
"Hajimemashite. Doozo yoroshiku." = How do you do? It's nice to meet you.
"Yoroshiku onegai shimasu." = It's nice to meet you, too.
Note: In the system of romanization used in this section, "ee" is not pronounced like feet. Instead, it means that the vowel sound "e" as in pet is prolonged. In the same manner, "oo" is pronounced not like shoot but as the "o" vowel, similar to pork, pronounced twice as long.