Q: When does the restricted takbir (al-Takbir al-Muqayyad) begin?
A: The restricted takbir is that which is associated with al-Adha and said after every obligatory prayer performed in congregation.
The takir is made by saying "Allahu akbar Allahu akbar la illaha illallah, wallahu akbar Allahu akbar wa lillahil hamd".
It begins, for the non-muhrim, at Fajr prayer on the day of Arafah (9th of Dhul-Hijjah, the day before Eid) and ends after Asr prayer on the 13th of Dhul-Hijjah.
The muhrim begins this takbir after Zuhr prayer on the day of Nahr/Eid and concludes the same time as mentioned above.
After prayer, the Imam should turn around and begin the takbir. It can be said one time up to three times.
If someone forgets to say it, they can make it up in the location where they prayed. If they got up to leave and then remember, they should return to their spot and make it up. If they make it up while walking, that too is fine. If they leave the masjid, break their wudu, or allow too much time to lapse before they remember, it is forgone.
If the Imam forgets to say it, the congregant should say it so as to not miss out on the reward.
If someone is late to prayer, it is recommended to say it after they complete what is missed.
It is not recommended after Eid prayer.
Source: Sharh al-Muntaha