Takbir is a very important act during times of pilgrimage and days involved, so the Prophet (PBUH) used to increase takbir during this period of time, especially during days of Arafa, An-Nahr and Tashriq, namely eleventh, twelfth, and thirteenth. Al-Bukhari stated: `Umar, may Allah be pleased with him, used to make Takbir inside his tent at Mena, and people of the mosque hear his Takbir, thus they make Takbir also, and people at markets make takbir accordingly so that Mena throbs of Takbir. Also, ibn Umar used to make takbir at Mena during these days after regular prayers, in bed, tent, and everywhere he goes.

Maymuna, may Allah be pleased with her, used to make takbir at the day of Nahr, and women used to make takbir following aban ibn Uthman and Umar ibn Abdulaziz at nights of Tashriq at mosques with men.

Wording of Takbir is: Allah is the Greatest, Allah is the Greatest, there is no true god except Allah, Allah is the Greatest, Allah is the Greatest, and all praise is due to Allah. Sunnah of the Prophet (PBUH) shall be made after the regular prayers, it is more likely to start after Fajr prayer of Arafa Day, and ends by the noon prayer of the thirteenth of Dhulhijjah, namely the third day of Tashriq.

It is a sunnah to make takbir in a loud voice. Takbir makes Muslims feel inner strength as they find everything in the whole life tinny behind Allah Almighty.

https://en.islamstory.com/en/artical/28804/99-sunnah-takbir-days-arafa-nahr-tashriq