Well, if you want to be very polite, you could use:
はじめまして (hajimemashite) - Nice to meet you
[Say your name] ともうします([your name] to moushimasu) - I'm called [--]
よろしくおねがいします (yoroshiku onegaishimasu)
Other less formal way is
はじめまして (hajimemashite)
[Say your name] といいます // という ([your name] to iimasu / to iu)
* "to iu" is more casual
よろしくおねがいします (yoroshiku onegaishimasu)
And there is the standard way:
はじめまして (hajimemashite)
[Say your name] です ([your name] desu) - I'm [--]
よろしくおねがいします (yoroshiku onegaishimasu)