Akemashite Omedetou Gozaimasu
is the most common greeting used by every Japanese for New Year.
It is very polite but most commonly used between friends, family members, business acquaintances, etc. when we meet each other first time in new year.
However, amongst young people or between very close friends, they say the abbreviation phrase such as “Ame Ome Koto Yoro” (which we do not recommend you to use it though).
Koto Yoro is the abbreviation of Kotoshimo Yoroshiku Onegaishimasu (very polite), which means roughly “stay friendly this year too”.
Enjoy speaking Japanese!!