Beginning the day after Rosh Hodesh Elul (the month before Rosh Hashanah), and concluding the day before Yom Kippur, Selihot are recited early each weekday morning before shahrit. These are special prayers designed to facilitate Teshuva (repentance). It is inappropriate to arrive at the annual Day of Judgment, as Rosh Hashanah is called, without having prepared beforehand.
Rosh Hashanah, the beginning of the Jewish year, is the Day of Judgement. One must be serious and not engage in lightheadedness. It is important to dress modestly.
Although it's the Day of Judgement, we are to express our confidence that the Al-mighty will accept our prayers and repentance and inscribe us for a year of life. Thus, it is prohibited to fast and the misvah of Simhat Yom Tov (happiness of the holiday) applies to Rosh Hashanah; there should be a festive meal.
During the evening meal, after kiddush and hamosi, we eat special foods that through their names or nature prompt optimistic thoughts for the New Year. We say an appropriate prayer for each. Some communities have this custom only the first night, some both nights. It is customary to dip the hamosi in sugar or honey instead of salt and not eat "sour" dishes throughout Rosh Hashanah.
The beracha of shehehiyanu is recited in kiddush both nights just as on both first nights of all yamim tovim. However, Shulhan Aruch states it is preferable to have a "new" fruit on the table the second night and direct the shehehiyanu to it also, as there is a group of poskim who don't allow shehehiyanu the second night of Rosh Hashanah, considering the two days as one long day halachically. If one does not have a "new" fruit, shehehiyanu is still recited.
In some respects, the two days of Rosh Hashanah are considered as a single halachic day; thus the lenient halakha regarding the use of medicines on the second day of Yom Tov does not apply to the second day of Rosh Hashanah. Even in Israel Rosh Hashanah is celebrated two days, unlike other yamim tovim.
It is preferable not to sleep during the day of Rosh Hashanah, but rather to study Torah. If one finds himself in a situation where he cannot concentrate on studying Torah and is gossiping, it is preferable to sleep.
It is traditional to sing with special high holiday melodies poetic works of great rabbis on the exalted themes of Rosh Hashanah and Yom Kippur. Rosh Hashanah is ushered in with the singing of "Ahot Ketana".
The amida of Rosh Hashanah and Yom Kippur emphasizes the kingship of the Al-mighty and includes additions reflecting the vision of a world in harmony and peace fulfilling His will.
It is customary to have assistants to the right and left of the hazzan during the prayers of Rosh Hashanah and Yom Kippur.
Additions to Prayers: Hashem Hu Haelokim is recited before Hashem Melech, Shir Hamaalot imaamakim is recited after Yishtabah, Avinu Malkenu is recited after the amida of shahrit and minha. Hamelech Hakadosh is said in place of Hakel Hakadosh in the amida. Several additional insertions are made in the amida as found in all mahzorim.
Torah and Haftarah Readings: On the first day the Torah reading begins with Hashem's "remembering" Sarah (with childbirth). A portion about Rosh Hashanah is read from a second Sefer Torah. The haftarah is about Hashem's `remembering' Hannah. The second day Torah reading is Akedat Yishak. The portion read from the second Sefer Torah is the same as the first day. The haftarah, from the prophet Yirmiya, is about Hashem's remembering, and love for, Israel.
Musaf: The musaf prayer of Rosh Hashanah includes three special sections reflecting the essence of the day. Each section comprises ten verses from the Tanach and concludes with a beracha.
The first section focuses on G-d's kingship; the second on His remembrances for judgement; the third on the significance of the shofar.
Tashlich: In the afternoon of the first day we go to the banks of a body of water and recite "Tashlich", a symbolic "casting away of sins". If a natural body of water is not available, it is acceptable to fill a pool. One who did not recite this prayer on Rosh Hashanah should do so during Asseret Yeme Teshuva.
It is a Torah commandment to hear certain Shofar blasts on the day of Rosh Hashanah. In the Books of the Prophets the shofar is associated with the signal of the city watchman who warns that the enemy is arriving. On the Day of Judgment the Shofar is the alarm that we are faced with an emergency; it awakens us from our slumber and calls us to repent.
The shofar also recalls the ram substituted for the sacrifice of Yishak. It is also associated with the Giving of the Torah, Resurrection, the Ingathering of the Exiles and the glory of the King.
Women are not obligated to hear the shofar as it is a positive misvah governed by time. Nevertheless, they fulfill a misvah if they hear it.
Children who have reached the age of understanding should be brought to synagogue to hear the shofar but only if they don't disturb others.
The Tokeah (shofar blower) should stand. For the first series of blasts the congregation remains seated.
The Tokeah must intend the blowing for the misvah and have the intent that others may fulfill their obligation through hearing his blowing. The listener must also have intent to fulfill his obligation.
Two berachot are recited before blowing the shofar the first time: "Lishmoah Kol Shofar" and "Shehehiyanu". One who has fulfilled his obligation of shofar earlier in the day and is blowing only for others may still recite the berachot.
The complete misvah comprises 100 individual blasts. They are blown in eight series. The first series, before musaf, comprises 30 blasts. The other seven series comprise ten blasts each: three series in the quiet amida, three in the hazara and one in the kaddish after the amida. It is customary to blow a 101st blast, a teruah gedola, before Alenu.
When Rosh Hashanah occurs on Shabbat the shofar is not blown and it is "mukseh". Although from Torah law the shofar should be blown even on Shabbat, the rabbis prohibited it, fearing it might lead to carrying on Shabbat.