Prophet Muhammad ﷺ said
“There are no other days that are as great as these in the sight of ALLAH and no acts are more beloved to ALLAH than those in these ten days”.
Recite Takbirat
الله أكبر الله أكبر لا إله إلا الله الله أكبر الله أكبر ولله الحمد
Things to do
Here are the list of things we can do make these 10 days blessed for us.
1- Standing the night in prayer
Seeking Allah’s forgiveness and humbling ourselves in front of Him in supplication and prayers during the latter part of the night is an act of worship that is very beloved to Allah
2- Fasting
It is Sunnah for the Muslim to fast on the first nine days of zilhajj, because fasting is one of the best of deeds.
ALLAH says :
“All the deeds of the son of Adam are for him, except fasting, which is for Me and I shall reward for it.” [Bukhari, 1805]
The Prophet said:
“Fasting the day of `Arafah expiates the sins of two years: the past one and the coming one.” [Muslim]
3- Quran
Read Quran in 10 days as much as you can, even if it is a verse. Reading the Quran is a good deed, ALLAH loves the good deeds done in these days.
4- Zhikr & Dua
Do zikhar and Dua in these 10 days. These 10 days has so much significance and blessings. Try to get maximum blessings from ALLAH by doing Zikhar and Dua.
Takbir : ALLAH-hu-AKBAR (ALLAH is Greater)
Tahleel : Laa ilaha ill-Allah (There is no god but Allah)
Tasbeeh : Subhaan-Allah (Glory be to God)
5- Charity
ALLAH loves charity. Give charity in these blessed days to get more reward from ALLAH.
“If ye loan to Allah a beautiful loan, He will double it to your (credit), and He will grant you Forgiveness: for Allah is Most Ready to appreciate (service), Most Forbearing.”
6- Eid & Sacrifice
Qurbani is the sacrifice of an animal for ALLAH during Eid ul-Adha. It is the sunnah of Prophet Ibrahim 
. It is a means of getting closer to Allah 
. It is obligatory for the person who has wealth equal to or more than nisab. It is performed on the days of sacrifice which is the 10th, 11th,12th of Dhul Hijjah.
Allah says in the Qur’an:
It is not their meat, nor their blood, that reaches Allah, It is their piety that reaches Allah.”