(Based on Hanafi School of Islamic fiqh)
Eid is a special occasion and one of the things which makes it so is the Eid-ul-Adha congregational prayer.
Since this prayer comes only once a year, there is often confusion about how to perform this prayer. Here is how to do it:
In general, when praying any Salah, always follow the Imam in prayer. Do not make your movements (i.e. bowing, prostrating, etc.) before he does or different from him.
Eid prayer consists of two units (Rakat in Arabic, singular is Raka). The main difference in the way this prayer and any other prayer of two Rakat is performed is the number of Takbirs that are done.
Takbirs is an the Arabic word referring to when "Allahu Akbar" is said and the hands are raised to the ears.
Step 1: Make an intention of doing two Rakat behind the Imam for Eid prayer along with six additional Takbirs.
The First Raka
Step 2: After the Imam has said "Allahu Akbar" the first time, you should raise your hands and follow. This is the first Takbir of the prayer.
Step 3: There will be 3 Takbirs before the Imam starts reciting Quran. Each time the Imam says "Allahu Akbar", you should follow by raising your hands, then putting them on your sides.
After the third Takbir, the Imam will begin reciting the Quran. At that point, you should put your hands on your chest, with your right hand on top of the left.
Step 4: Listen to the recitation of the Holy Quran. The Imam will recite Surah Al Fatiha (the first Surah of the Quran) and then another Surah.
Step 5: When the Imam says "Allahu Akbar" go into Ruku (the bowing position).
Step 6: Stand up straight when he says Sami Allahu liman Hamidah (Allah hears those who praise Him), and say "Rabbana lakal Hamd" (our Lord praise be to You) in a low voice.
Step 7: When the Imam says "Allahu Akbar" go into Sujud (prostration). You will do two prostrations as in normal prayer.
The Second Raka
Step 8: The Imam will first recite from the Holy Quran (first Surah Al Fatiha and another Surah.
Step 9: After the recitation, before going into Ruku, there will be 3 Takbirs. Follow the Imam. Raise your hands after each "Allahu Akbar". After the third Takbir, go into Ruku (the bowing position).
Step 10: Stand up straight when the Imam says Sami Allah huliman Hamidah, and say "Rabbana lakal Hamd" in a low voice.
Step 11: When the Imam says "Allahu Akbar" go into Sujud. You will do two prostrations.
Step 12: After this, you sit for the complete Tashshahud.
Step 13: After the Imam ends the prayer by turning to his face to the right first and saying "Assalamu alaikum wa Rahmatullah" and then to his left and doing the same, you should follow.
Step 14: Do not get up right away. The Imam will give a short Khutbah (speech). Please stay still and listen. It is recommended to do so.