Русский
Russian Self-Introduction Phrase: "Приятно познакомиться"
"Приятно познакомиться" (Priyatno poznakomitsya) is the standard Russian way to say "Nice to meet you," literally meaning "It's pleasant to get acquainted." It's natural to say while shaking hands right after introducing yourself. You can reply with the same phrase, or "Мне тоже" (Me too).
Examples
Меня зовут Иван. Приятно познакомиться.
"My name is Ivan. Nice to meet you." (a common thing to add right after saying your name)
Мне тоже приятно.
"It's nice for me too." (a typical reply to "Приятно познакомиться")
Очень приятно.
"Very nice." (a simpler way to say the same thing)