The Month of Elul
2. It is customary to blow the shofar during the month [of Elul], beginning on the second day of Rosh Chodesh Elul (1).
Each day, after the morning service, the shofar is sounded in the following order: Teki'oh, Shevorim, Teru'oh, Teki'oh. On the day preceding Rosh HaShanah, however, the shofar is not sounded, in order to differentiate between the sounding of the shofar [as a custom which is] voluntary ("reshus"), and the sounding of the shofar as a mitzvah (that is, a Biblical obligation).
The rationale for sounding the shofar during this month is to motivate people to repent, for the very sound of the shofar has a tendency to arouse awareness and inspire fear, as [Amos 3:6] states: "Shall a shofar be sounded in the city and the people not tremble?"
In our local areas (2), it is also customary to add [Psalm 27,] "L'Dovid, Hashem Ori ve'yishi'i..." at the end of the prayer service in the morning and in the evening, from the second day of Rosh Chodesh until Shemini Atzeres (3)
The source for this custom is the Midrash [Sochor Tov], which explains the opening verse of the psalm as follows: "G-d is my light" on Rosh HaShanah and "my salvation" on Yom Kippur. The psalm also has an allusion to the festival of Sukkos: "For He will hide me in His sukkah." It is also customary to recite Psalms communally during this month, each community according to its local custom.
When a person writes a letter to a colleague from the beginning of Elul until Yom Kippur, it is proper, at the beginning or conclusion of the letter, to include wishes and blessings that one's colleague be judged favorably in the approaching days of judgment, and be inscribed and sealed for a good life,
(1) Some have the custom to begin blowing the shofar on the first day of Rosh Chodesh.
(2) Hungary in the late 19th Century.
(3) There are several differences between the ruling of the "Kizur Shulchan Oruch" and the prevailing custom in some communities. Firstly, there are some communities that begin the recitation of "L'Dovid Hashem..."from the first day of Rosh Chodesh Elul. Secondly, in certain communities, it is customary to recite the psalm in the afternoon service rather than in the evening service. Also, in Eretz Yisrael, the Psalm is not recited on Shemini Atzeres itself.