Ten Days of Dhul Hijja
Even for those not performing the pilgrimage, Hajj, the first ten days of this month are considered very sacred and a time for increased reflection, seeking Allah's forgiveness, doing good and various other forms of worship.
Prophet Mohammed (peace and blessings be upon him) has said about the first ten days of Dhul Hijja: "There are no days in which righteous deeds are more beloved to Allah than these ten days." The people asked, "Not even Jihad for the sake of Allah?" He said, "Not even Jihad for the sake of Allah, except in the case of a man who went out to fight giving himself and his wealth up for the cause, and came back with nothing (Bukhari).
While any good deed done for the sake of Allah according to the way He approves will be rewarded immensely during the first ten days, Insha Allah, some of the more specific actions mentioned in the Traditions of the Prophet are as follows:
In terms of fasting, it is particularly encouraged to fast on the ninth day of Dhul-Hijja, known in Arabic as Yawm Arafa. The Prophet used to fast on this day (al Nisai and Abu Dawud). Fasting on this day will expiate a Muslim's sins for two years.
The verbal remembrance of Allah is another meritorious act during these first ten days of Zul Hijjah. The Prophet upon him) encouraged Muslims to recite a lot of Tasbeeh ("Subhan-Allaah"), Tahmeed ("Al-hamdu Lillaah") and Takbeer ("Allahu akbar") during this time.
The Takbeer may include the words "Allahu akbar, Allahu akbar, la ilaha ill-Allah; wa Allahu akbar wa Lillahiíl-hamd (Allah is Most Great, Allah is Most Great, there is no god but Allah; Allah is Most Great and to Allah be praise)," as well as other phrases.
Men are encouraged to recite these phrases out loud and women quietly.
One of the good deeds that will bring a person closer to Allah during these ten days is offering a sacrifice, by choosing a high-quality animal and fattening it, spending money for the sake of Allah.
4. Sincere repentance
One of the most important things to do during these ten days is to repent sincerely to Allah and to give up all kinds of disobedience and sin. This means more than just a verbal expression of sorrow for past misdeeds. It also requires a firm resolution to avoid making the same mistakes in the future by giving up bad habits and behavior while sincerely turning to Allah.
Generally, all good deeds are rewarded highly at this blessed time. These actions include praying, reading Quran, making Dua (supplication), giving in charity and being good to our families.
"The first 10 days of Zul Hijjah: why they matter" - SoundVision.com
"Virtues of the Ten Days of Dhul Hijjah" - Salih Al Munajjid