expression
Polite New Year's greeting used from January 1st onward. The phrase literally means 'congratulations on the opening (of the new year)'. It is the standard formal greeting for the new year period.
明けましておめでとうございます。今年もよろしくお願いします。
Happy New Year. I look forward to your continued friendship this year.
新年のご挨拶：明けましておめでとうございます。
New Year's greeting: Happy New Year.
Casual, shortened slang form of 明けましておめでとう, used among friends. Not appropriate in formal situations.
Casual, shortened slang form of 今年もよろしくお願いします, often paired with あけおめ.
Formal written New Year's greeting, typically used on postcards or in formal letters. More stiff and traditional than 明けましておめでとうございます.
From 明ける (akeru, 'to dawn, to begin') in its continuative form 明けまして (akemashite) + おめでとう (omedetou, 'congratulations') + ございます (gozaimasu, polite copula). The phrase literally means 'congratulations on the beginning (of the new year)'.