128:2 The practice is to blow the shofar during the month of Elul, starting on the second day of Rosh Chodesh. We blow the shofar every day after shacharis as follows: tekiah, shevarim, teruah, tekiah. We do not blow shofar on the day before Rosh Hashana; we stop in order to separate between the voluntary shofar-blowing of Elul and the Torah obligation of Rosh Hashana. The reason the shofar is blown during the month is to arouse the people to repent. The nature of the shofar is to raise people’s awareness and to instill fear, as per Amos 3:6, “Can a shofar be blown in the city and the people not tremble?”
The practice is also to recite L’David (Psalm 27) from the second day of Rosh Chodesh Elul until Shemini Atzeres (inclusive – Mishnah Brurah 581:2) at the end of shacharis and maariv. This reason for this practice is that the words “G-d is my light” are said to refer to Rosh Hashana, “my salvation” to Yom Kippur, and “He will conceal me in His succah” to Succos. It is also customary to recite Psalms communally, each place according to its local practice. From the start of Elul until Yom Kippur, when a person writes a letter to a friend, he must include good wishes for the recipient and blessings that he be inscribed and sealed in G-d’s book for a good life,
128:3 Diligent people are in the practice of having their tefillin and mezuzos checked in Elul. Any problems that are found with any other mitzvos should likewise be rectified.