The Judaism editors of Wikipedia do a fantastic job as evidenced by this excerpt in the entry on Elul:
During the month of Elul, there are a number of special rituals leading up to the High Holy Days. It is customary to blow the shofar every morning (except on Shabbat) from Rosh Hodesh Elul (the first day of the month) until the day before Rosh Hashanah. The blasts are meant to awaken one’s spirits and inspire him to begin the soul searching which will prepare him for the High Holy Days. As part of this preparation, Elul is the time to begin the sometimes-difficult process of granting and asking for forgiveness. It is also customary to recite Psalm 27 every day from Rosh Hodesh Elul through Hoshanah Rabbah on Sukkot (in Tishrei).
We’ve been hearing the Shofar for about a week now and I’m sure many readers of Beyond BT have begun preparing for Rosh Hashanah by trying to take little steps of improvement.
Rabbi Welcher recently gave a shiur on the topic of “The Shofar of Elul”, where he discussed the minhagim and some practical ideas to take advantage of this powerful period in the Jewish calender. The shiur on the Shofar of Elul can be downloaded here.