The first ten days of Dhul Hijjah are blessed and special. The Messenger of Allah (blessings and peace be upon him) said:
“There are no days in which righteous acts are more beloved to Allah than in these days – meaning the ten of Dhul Hijjah.” [Bukhari]
Below are some of the acts we can perform during these blessed days.
It is recommended to fast during the first nine days of Dhul Hijja before Eid comes. Especially emphasized is the fast of the Day of `Arafah (9th of Dhul Hijjah).
The Messenger of Allah (blessings and peace be upon him) said:
“Fasting the Day of `Arafah expiates for two years, one prior and one forthcoming.” [Muslim]
Use these days to improve your prayer, read the Quran, and make dhikr. The Prophet (blessings and peace be upon him) said:
“There are no days that are greater before Allah or in which good deeds are more beloved to Him, than these ten days, so recite a great deal of tahlil, takbir and tahmid during them.” [Ahmad]
Tahlil is the phrase "Laa ilaaha illaLlaah" (there is no god but Allah), takbir is "Allahu akbar" (Allah is greater), and tahmid is alhamduliLlaah (All praise belongs to Allah).
Allah the Most High says:
"So pray to your Lord and perform the sacrifice" [Quran, 108:2]
The Eid prayer happens in the morning of the 10th day shortly after the sunrise (check the exact time in your local mosque). It is wajib (obligatory) for men to attend the prayer in the mosque, unless you are travelling, sick, or there is no Masjid in your town.
The sacrifice (or udhiya) means sacrificing an animal (sheep or cow) on Eid al-Adhha after the prayer. In Hanafi madhhab, udhiya is obligatory for every sane, adult Muslim who is not a traveler, and owns wealth beyond nisab. For more details check this article.