Kiddush is usual the Shalosh Regalim Kiddush, with reference to Shemini Atzeres.
We eat our festive seuda in the house, as the second day of this Yom Tov in the golah is considered like Shemini Atzeres in Eretz Yisrael – and this is not treated as a doubtful day (sefeka de’yoma).
Tuesday Morning: Shacharis – Shalosh Regalim tefilla – the Kohanim go up to the duchan during the chazzan’s repetition of the Shacharis Shemoneh Esreh. (The Levi’im, or where there are no Levi’im, the firstborn, wash the hands of the Kohanim before the chazzan reaches Retzeh.) We do not say Ve’se’arev, we do not say Ribbono Shel Olam and Yehi Ratzon. Chazzan and congregation now continue with whole Hallel. Chazzan concludes with Kaddish Tiskabbel.
Those who are so honored each read aloud a pasuk in Ata Horeisa – and then we remove the Sifrei Torah from the Ark. With all the Sifrei Torah removed from the Ark we now begin the Hakafos of the Bimah– we circle seven times in joyous dance. We then read in Parashas Vezos Haberacha (Deuteronomy 31:1-26). We divide the parasha into five aliyos, and we continuously to call people – repeating the keriah many times until all members of the congregation have been called.
We then call the person who was honored with Chassan Kol Hane’arim. He says the berachos with all the children under the canopy (or tallis), he is followed by the Chassan Torah who completes the year’s Torah reading (from Deuteronomy 31:27-34:12) to the end of Parashas Vezos Haberacha.
We call the Chassan Bereishis who reads from Parashas Bereishis (Genesis 1:1-2:3). Following the hagbaha and placing of the Sifrei Torah on the bima, ba’al keriah recites half Kaddish.
We finally call the Maftir who reads from Parashas Pinchas (Numbers 29:35-39; 30:1).
The Maftir then reads the Haftara (Joshua 1:1-18).
We say Ashrei and Sisu vesimchu besimchas Torah. Many add Hiskabtzu and Agil Ve’esmach.
We return the Sifrei Torah to the Ark and the chazzan recites half Kaddish.
Musaf: in both the silent Shemoneh Esreh and the chazzan’s repetition, the tefilla is that of Shalosh Regalim – all references again, are to Shemini Atzeres. There is no duchaning at Musaf, as we have already done so during Shacharis. Chazzan then concludes with Kaddish Tiskabbel. This is followed by Ein K’Elokeinu, Aleinu, Shir Shel Yom (some congregations add An’im Zemiros) and the respective Kaddish recitals.
Mincha: Ashrei, U’va LeTziyyon, Shemoneh Esreh of Shalosh Regalim.
Ma’ariv: The earliest zeman is 45 minutes after sunset, that is, 6:45 p.m. (N.Y.C., E.D.T.), Maariv prayer is usual weekday Maariv with Ata chonantanu. Havdala is over wine, no flame or spices.
We do not say Tachanun until after Rosh Chodesh (2 Marcheshvan).
The following chapters of Tehillim are being recited by many congregations and Yeshivos for our brothers and sisters in Eretz Yisrael: Chapter 83, 130, 142 – Y.K.