Many congregations conclude the service with the chanting of Adon Olam. Following the Seudas Yom Tov we return to the synagogue for Mincha (no reading of the Torah). The Shemoneh Esreh (text in the Machzor) is followed by Avinu Malkenu, Kaddish Tiskabbel, Aleinu and Kaddish Yasom (Mourner’s Kaddish).
It is customary on Rosh Hashana to go near – or at least in sight of – a river, stream or pond and recite the Tashlich prayer. It is also customary to say additional prayers for parnasa and health as found in the Machzor. [This Tefillah may be said during the week if necessary.]
Monday evening, the second night of Rosh Hashana: since we are not allowed to make any preparations from one day of Yom Tov to the other, we wait 45 minutes after Shekia (N.Y.C. E.D.T. time 7:51 p.m.) some wait 60 minutes (N.Y.C. time: 8:06 p.m. E.D.T.) while others wait 72 minutes (N.Y.C. time: 8:18 p.m. E.D.T.) before we light candles and then we commence all preparations. When lighting candles we recite Lehadlik Ner Shel Yom Tov, and Shehecheyanu (R. Henkin rules that it is better to prepare a new fruit to eat at the seuda, and for the woman of the house to light as close to Kiddush as possible, thus eating the new fruit close to her lighting and reciting the Shehecheyanu).
Maariv: The text as found in the Machzor, Birkas Kerias Shema (concluding Hashkivenu with U’feros … Ve’al Yerushalayim). We add Tik’u bachodesh shofar bakeseh le’yom chagenu. At the conclusion of the Shemoneh Esreh the chazzan recites Kaddish Tiskabbel (Nusach Sefarad say LeDavid Mizmor). Where such is the custom, Kiddush is recited by the chazzan (Rosh Hashana text as in the Machzor), Aleinu, and LeDavid Hashem Ori and respective Kaddish recitals for mourners. Kiddush at home is the same as in the synagogue and, as mentioned previously, we place a new fruit on the table for the blessing of Shehecheyanu (if one dons a new garment, it is just as well), which is recited regardless of the availability of these new items.
Tuesday morning: Shacharis is generally the same as the day before, with certain variant texts for Piyyutim and Yotzros as found in our Machzor. Avinu Malkenu at the conclusion of the repetition of the Shemoneh Esreh. There are various customs: most Sefarad congregations and some Ashkenaz say the Shir Shel Yom and LeDavid at this point, followed by the respective mourner’s Kaddish recitals.
We call up five people to the Torah and we read in Parashas Vayera (Bereishis 22:1-24), following which the Ba’al Keriah recites half Kaddish. For Maftir we read in Parashas Pinchas like yesterday (Bamidbar 29:1-6). The Maftir reads the Haftara, Matza chen bamidbar (Jeremiah 31:1-19). In the blessing for the Haftara, as we did yesterday, we add Yom Hazikaron Hazeh, and conclude with Mekaddesh Yisrael VeYom Hazikaron.
Tekiyas Shofar, Musaf, Mincha, see 1st day Yom Tov. Note: Some of Piyutim in Musaf for 2nd day are different.
Motza’ei Yom Tov: Maariv is the usual weekday tefilla. We say Ata Chonantanu and add the Aseres Yemei Teshuva – Days of Awe – textual changes (i.e., HaMelech Hakadosh, etc.). (Yom Tov concludes in N.Y.C. at 7:52 p.m. E.D.T.)
For the havdala we use neither a candle nor besamim (spices). We use only wine and begin with the blessing of Borei Pri Hagafen and conclude with the blessing of Hamavdil.
Wednesday is Tzom Gedalia – a public fast (starting at 5:25 a.m. N.Y.C. E.D.T.) instituted by our sages due to the assassination of Gedalia ben Achikam, the Judean governor of Eretz Yisrael appointed by the Babylonians, and its significance for our subsequent dispersal in the diaspora.