935. Havdalah after Yom Kippur

133:27 After the stars come out, we recite maariv. (We have to wait a small interval in order to add from the holy day to the secular day. During this interval, we may not eat, wash or anoint. After davening maariv, one may wash, anoint, etc. even if he has not yet heard havdalah recited over a cup. Eating and drinking, however, require hearing havdalah over a cup - Mishnah Brurah 624:3.) We should have an appropriate shaliach tzibbur, who will pray pleasantly and with concentration; we should rebuke those who rush. In Shemoneh Esrei, we say, "Atah chonantanu" (which is a form of havdalah said in prayer).  If Yom Kippur was on Shabbos, we recite "V'yiten L'cha" in maariv but not "Vayehi Noam" or "v'Atah Kadosh." After maariv, we sanctify the moon (weather permitting) and exchange friendly greetings with rejoicing and gladness as we do on holidays.

133:28  At havdalah following Yom Kippur, we only bless over a candle that "rested," not on a candle that was lit from a fire struck now for this purpose. The best way is to light a candle from the candle that one lit in his house before Yom Kippur and to recite the bracha over both of them. If one does not have a light in his house, he may bring the candle that he lit in shul, light his candle from this and recite the bracha over them. In a pinch, one can recite the bracha over a candle that was lit by a non-Jew or that he struck from a match, etc. (It's best to light a candle before Yom Kippur specifically for the purpose of providing fire for havdalah. -  Mishnah Brurah 624:13. If one recited havdalah only over a candle that burned all Yom Kippur, even though he shouldn't have, he need not repeat it - MB 624:14. Bi'ur Halacha recommends against relying on the minority opinion that allows one to strike a fire - 624:4 s.v. v'yeish omrim.) Havdalah does not begin with "Hinei Keil Yeshuosi" as it does on Saturday nights.  Rather, one recites the bracha over the wine, then the bracha over the light and, finally, the bracha of HaMavdil. Spices are not used after Yom Kippur unless it was also Shabbos. (In such a case, spices are used at home but not in shul - MB 624:5.) In that event, one would also start with "Hinei Keil Yeshuosi" as per usual.