It is accustomed amongst all Jewry to increase in charity, good deeds and to involve oneself in Mitzvos throughout the days between R”H and Yom Kippur.
One may say Tehillim at night during Aseres Yimei Teshuvah.
Buying a set of Lulav and Esrog:
Some write that one is to try to purchase a set of Daled Minim during Aseres Yimei Teshuvah in order to add in merits for the day of Yom Kippur and have these merits overturn the judgment. Others however write that one is specifically to buy the Esrog after Yom Kippur as the tears of Yom Kippur clean the blemishes of the Esrog.
Avoiding marital relations:
Some are accustomed to avoid marital relations during the 10 days of repentance unless it is the night of Mikveh. Certainly however one is not avoid doing so if he feels his inclination overpowering him.
The custom is to avoid making weddings of a 1st marriage between Rosh Hashanah and Yom Kippur. However a 2nd marriage may be made during these days. In a time of need a couple may marry even a 1st marriage during this time.
The 6th of Tishrei is the day of the passing of the Rebbe’s mother. She passed away in 1965.
 Rambam Hilchos Teshuvah 3/4; Kaf Hachaim 602/4
 Sefer Haminhagim p. 41 [English]
 Kitzur SH”A 130/6; Mateh Efraim 603/5
 Shem Meshmuel [Sukkos]; Drashos Chasam Sofer 38a brought in Piskeiy Teshuvos 602/4
 Or Tzaddikim 27/11; Siddur Arizal of Rav Shabsi; Beir Heiytiv 240 in name of Kneses Hagedola; Piskeiy Teshuvos 603 footnote 2
 M”B 240/7
 Mateh Efraim 602/5; Chochmas Shlomo 602; Igros Kodesh Vol 9 p. 205; Piskeiy Teshuvos 602/3
The reason: The reason for this is because a) The moon is considered concealed until after Yom Kippur, and when the moon is concealed one is to avoid getting married. B) When married all one’s sins are forgiven. It is not proper to precede G-ds forgiveness on Yom Kippur with a personal loophole in which he gets forgiveness. [Chochmas Shlomo ibid]
Other opinions: Some communities however have never accepted this custom, and thus make weddings during these days. [Yechaveh Daas 1/48]
 Alef Hamagen 602/5
 M”E ibid