There is some confusion about what one should wish people on Yom Kippur. Chag Sameach (happy festival), or Moadim lsimchah (occasions for joy), are not quite right. Yom Kippur has an aspect of simchah, joy, in that it is a time of forgiveness, but joy is restrained by awe at the Day of Judgment.

Good Yomtov is always a safe bet, and Gmar chatimah tovah, May you be sealed for good (in the coming year), is quite correct.

Shanah Tovah, A good year, is also appropriate. The Hebrew word shanah has two associations that appear contradictory. On the one hand, it means to repeat, or to do a second time (related to sheni, the number two.) The Jewish year is a cycle of sacred times that is repeated endlessly. On the other hand lshanot means to change, modify or distinguish. The repetition provides an annual chance for change.

Yom Kippur is an opportunity to decide that next year will be different from last year. By resolving to do things differently and sincerely regretting the past, we can, with Gods help, break free of the endless chain of consequences that our mistakes set in motion and make the years repetition a chance for transformation.