The Eid Prayer is obligatory under certain conditions, and its time is sunrise till noon. It is prayed in congregation. Women are exempted from this prayer, but if they are inclined there is no restriction for them to pray.
In the first rakaat, after reciting al-Hamd and another surah, (preferably surah A'ala) recite takbir and raise your hands to recite qunut.
After finishing, recite takbir and qunut again. Repeat for a total of five takbirs and qunuts.
After the fifth qunut, recite takbir and then perform ruku (bowing) and two sajdahs (prostration) and stand erect. This completes one rakaat.
In the second rakaat, after reciting al-Hamd and one other surah, (preferably surah Shams), recite takbir and qunut four times in the same manner as in the first rakaat and complete the prayer as usual.
After prayer, the Imam (prayer leader) recites two Khutbas (sermons).
Note: The Eid prayer unlike the 5 daily prayers is not preceded by Adhan or Iqamah, but it is recommended to call thrice As-Salaat (To Prayer).
اللهم اهل الکبریاء و العظمة و اهل الجود والجبروت و اهل العفو والرحمة و اهل التقوی والمغفرة اسئلک بحق هذا الیوم الذی جعلته للمسلین عیدا و لمحمد صلی الله علیه و آله ذخرا و مزیدا ان تصلی علی محمد و ال محمد و ان تدخلنی فی کل خیر ادخلت فیه محمدا و ال محمد و ان تخرجنی من کل سوء اخرجت منه محمدا و ال محمد صلواتک علیه و علیهم
«O Allah, Lord of magnificence and greatness and Lord of generosity and overwhelming power; and Lord of pardon and mercy. We implore You for the sake of this day which You have appointed as a Festival for the Muslims and for Muhammad (s) and his progeny as a reminder, a distinction, an honour, to bless Muhammad and his progeny and admit me to all the bounties to which You have admitted Muhammad and his progeny, and keep me away from all evils from which You have kept away Muhammad (s) and his progeny. May Your blessings be upon him and his progeny. i beg of You of the best which has been asked for by Your virtuous good servants, and I seek Your protection from all those evils from which Your sincere servants have sought Your protection.»
It is preferable to go to the Mosque for Eid Prayer. If this is not possible then one should say the prayer at home, in the manner described above. If this is not possible, then recite it like the morning prayers, but in the first Rakaat recite Qunut (whatever you know) 5 times, and in the second Rakaat 4 times.
Ghusul (bath) on Eid day is optional which should be taken under a shelter and not under the open sky.
Praise be to Allah, Lord of the worlds.