In Hebrew, the common way to say "Happy New Year" is "Shanah Tovah" (שנה טובה), which literally means "Good Year." Another phrase that is often used to wish a "Good and Sweet Year" is "Shanah Tovah Umetukah" (שנה טובה ומתוקה).
These greetings are especially used during Rosh Hashanah, the Jewish New Year, but they can generally convey the sentiment of a happy new year in Hebrew.
