Greetings for the end/beginning of year (年末年始の挨拶)

In Japan, when you meet someone in the end of year (about the second half of December) and never meet them in the year, you can say “Yoi otoshi wo!” instead of “See you!”. It means “Have a good new year!”

The polite and long version is “Kotoshi wa osewa ni narimasita. Douzo yoi otoshi wo omukae kudasai”. It means ”Thank you for your supporting me throughout the year. I wish you have a good new year”. But “Yoi otoshi wo” is polite enough to say it to people like your boss.

As for in the beginning of new year (about the first half of January), the standard greeting is “Akemashite omedetou gozaimasu”. It means “A happy new year”. If you say “Kotoshi mo yoroshiku onegai shimasu” after that, it will become more polite.

Young people usually say it for short like “Akeome! Kotoyoro!” to their friends. I say it to some of my friends too, but I think it’s too casual and insipid.
若い人はよくこれを短くして「あけおめ! ことよろ!」と友達に言います。私も一部の友達にはこれを言いますが、ちょっとくだけすぎて味気ないようにも思います。