During Eid, Muslims express their gratitude to Allah. They also visibly show joy and congratulate each other. On Eid, Muslims exchange gifts, which is another important sunnah for that day. Also, Muslims make lots of istighfar (asking Allah for forgiveness) and pray that Allah accept their good deeds. The Eid al-Fitr marks the completion of fasting the blessed month of Ramadan, the fourth pillar of Islam. The Eid al-Adha marks the completion of Hajj (Pilgrimage to Makkah), the fifth pillar of Islam. On Eid, Muslims chant the takbirat aloud, and this is one of the greatest Sunnahs (traditions) of Eid.
The takbirat are as follows:
اللَّهُ أَكْبَرُ اللَّهُ أَكْبَرُ اللَّهُ أَكْبَرُ
Allah is Most Great
Allahu akbaru-llahu akbaru-llahu akbar
لَا إِلَهَ إِلَّا اللَّهُ وَاللَّهُ أَكْبَرُ
There is no god except for Allah and Allah is Most Great
La ilaha ill-llahu wallahu akbar
اللَّهُ أَكْبَرُ وَلِلَّهِ الْحَمْدُ
Allah is Most Great and to Allah belongs all praise
Allahu akbaru walillahi-l-hamd

It is wajib to commence the takbir of tashriq after the dawn on the day of Arafah (9th Dhul Hijjah) and is to be ended after the ‘asr prayer on the final day of tashriq (13th Dhul Hijjah). It is to be pronounced once, straight after every obligatory prayer which is performed in a recommended group prayer.' And the takbir is wajib upon the imam who resides in the city and his followers even if they are travellers, slaves or females. However, the women are not to pronounce the takbir aloud. They are to utter the takbir silently and not audibly. As for the imam and those with him, they are required to utter it loudly. Moreover, it is necessary to join the takbir to the finishing salam of prayer. Allah said in Surah al-Hajj, verse 22: “Remember Allah during the known days”, and in Surah al-Baqarah, verse 203: “Remember Allah during the appointed days.” It is maintained that the appointed days (معدودات) are the days of tashriq and that the known days (معلومات) are the first ten days of the month of Dhul Hijjah.