Say Psalm 27 after alenu during Elul and most of Tishrei.  For more about Psalm 27, see When To Say Psalm 27/L'David Adonai Ori V'Yish'i.

Begin saying L'David Adonai ori v'yish'i (Psalm 27) on the first day (at night) of Elul, not the first day of Rosh Chodesh Elul (the 30th of Av). The last day to say this Psalm is 22nd of Tishrei (Shmini Atzeret). This Psalm is recited twice daily, in shacharit after shir shel yom and in ma'ariv after alenu, including on Shabbat and Jewish festivals.

It is customary not to say kiddush levana:

• During the Nine Days before and including Tish'a b'Av;
• On Friday night, and
• On the evening of a Jewish festival.

Many people also have the custom not to say kiddush levana during the first 10 days of Tishrei.
However, you should do so if you do not expect to see the moon on any other night (due to weather or other factors), rather than miss the chance to say it that month. If you do say kiddush levana on Friday night or the after nightfall of a Jewish festival, say only the blessing, not the Psalms and other phrases that are normally said.

Tachanun is related to judgment. Tachanun is NOT said at times of din/judgment:

• At night,
• On Tish'a B'Av,
• In a house of mourning, and
• Yom Kippur.

Tachanun is also NOT said at times of simcha/happiness:

• Shabbat,
• Jewish festivals,
• Rosh Hashana, and
• Rosh Chodesh.

• Isru chag (the day after each of the Jewish festivals),
• Entire month of Nisan.

• All of Chanuka, Purim, Shushan Purim, Tu B'Shvat, Rosh Chodesh, and from Rosh Chodesh Sivan until the day after Shavuot.
• Tishrei from shacharit before Yom Kippur until after Simchat Torah (Shmini Atzeret in Eretz Yisrael). Resume saying tachanun:
  • Second day of Cheshvan, or
  • Day after isru chag of Simchat Torah (this is the more prevalent custom among Ashkenazim). Each person should follow his or her family or community custom.

• Mohel,
• Sandak, or
• Father of a boy having his circumcision.