The Eid prayer has two raka'at performed in the normal way, with the only addition of six Takbirs, three of them in the beginning of the first raka'ah, and three of them just before ruku' in the second raka'ah. The detailed way of performing the Eid prayer is as follows:
The Imam will begin the prayer without Adhan or iqamah. He will begin the prayer by reciting Takbir of Tahrimah (Allahu Akbar). You should raise your hands up to the ears, and after reciting the Takbir, you should set your hands on your navel. The Imam will give a little pause during which you should recite Thana' (Subhanakallahumma .:.). After the completion of Thana', the Imam will recite Takbir (Allahu Akbar) three times. At the first two calls of Takbir you should raise your hands up to the ears, and after reciting Takbir (Allahu Akbar) in a low voice, should bring your hands down and leave them earthwards. But, after the third Takbir, you should set them on your navel as you do in the normal prayers.
After these three Takbirs, the Imam will recite the Holy Qur'an, which you should listen calmly and quietly. The rest of the raka'ah will be performed in the normal way.
After rising for the second raka'ah, the Imam will begin the recitations from the Holy Qur'an during which you should remain calm and quiet. When the Imam finishes his recitation, he will recite three Takbirs once again, but this time it will be just before bowing down for ruku'. At each Takbir you should raise your hands up to the ears, and after saying 'Allahu Akbar', bring them down and leave them earthwards. After these three takbirs have been called and completed, the Imam will say another takbir for bowing down into the ruku' position. At this takbir you need not raise your hands. You just bow down for your ruku' saying, 'Allahu Akbar'. The rest of the salah will be performed in its usual way.
Khutbah: The Address of Eidul-Adha
In this salah of Eid, Khutbah is a sunnah and is delivered after the salah, unlike the salah of Jumu'ah where it is fard and is delivered before the salah. However, listening to the khutbah of Eid salah is wajib or necessary and must be listened to in perfect peace and silence.
It is a sunnah that the Imam begins the first Khutbah by reciting takbir (Allahu Akbar) nine times and the second Khutbah with reciting it seven times.
The way of Eid prayer described above is according to the Hanafi school of Muslim jurists. Some other jurists, like Imam Shafi'i, have some other ways to perform it. They recite Takbir twelve times before beginning the recitations of the Holy Qur'an in both the raka'at. This way is also permissible. If the Imam, being of the Shafi'i school, follows this way, you can also follow him. Both ways are based on the practice of the Holy Prophet, Sall-Allahu alayhi wa sallam.