1. From the first of Ellul (the second day of Rosh Chodesh - the New Moon) until Hoshanah Rabbah inclusive, the Askenazi custom is to say Psalm 27 at the end of every morning and evening service (including on Shabbat).
Hassidim ( nusah sefarad ) say it in the afternoon service, instead of the evening service, and add the morning of Shemini Atzeret. This custom is based on the Midrash which interprets 'my light' (verse 1) as referring to Rosh Hashanah and 'my salvation' (same verse) as referring to Yom Kippur; 'he will hide me in shelter' (verse 5) is a reference to Succot (tabernacles, or shelters).

2. From the first of Ellul (the second day of Rosh Chodesh) until Erev (the eve of) Rosh Hashanah, (but not on Erev Rosh Hashanah itself,) the Shofar is blown every day (except on Shabbat) at the end of the morning service, before Psalm 27. Four sounds are blown: Tekiah, Shevarim, Teruah, Tekiah. These are a custom accepted throughout Israel, in contrast to the obligatory blowing on Rosh Hashanah, which is a law of the Torah.

3. 'As for me, my prayer to you, G-d, is at an acceptable time' (Psalm 69:14).
The most acceptable time is during the 40 days from the first of Ellul until Yom Kippur, so extra prayers are added during that period and a special effort is made to amend one's ways and deeds.

4. Before the modern system of hours was invented, the night was divided into three 'watches', each lasting on average about two hours, with the third being known as the 'morning watch'. It is customary to get up in the 'morning watch' to say Selihot prayers every day (except Shabbat and Rosh Hashanah) until Yom Kippur, because the morning watch is considered a time of acceptance, when 'G-d is near to all who call on him'. The first night some say the Selihot earlier, at midnight.
The Sephardim start reciting Selihot on the first of Ellul. Some start on the fifteenth. The Ashkenazi custom is to start them on the Sunday (or Saturday night) immediately preceding Rosh Hashanah, if the latter falls on Thursday or Saturday, and on the Sunday (or Saturday night) of the previous week if Rosh Hashanah falls on Monday or Tuesday. This ensures that they are said for not less than four days before Rosh Hashanah.

5. When writing a personal letter to someone during this period, it is customary to include a blessing for a satisfactory outcome on the approaching Days of Judgement. A reference to Job 26:7 is also included.

6. Many are particular to check their tefillin and mezuzot during Ellul.

7. On the last day of the outgoing year, Erev Rosh Hashanah, it is customary to annul vows, so as to enter the Day of Judgement and the new year without sin (or the liability to sin, caused by as yet unfulfilled vows).

8. No Birkat Hachodesh prayer for the coming month (Tishrei) is said on the Shabbat before Rosh Hashanah.

9. It is customary for those whose parents are no longer alive to visit their graves in the days before Rosh Hashanah. (In Israel, the custom is to visit the graves on the day before Rosh Chodesh Ellul and the day before Rosh Chodesh Nisan.)