Eids or festivals are moments of celebration common to all nations. The festivals of non-believing nations are associated with worldly matters such as the birth of a nation or its decline, the appointment or crowning of a ruler, his marriage, or the beginning of a season like spring, and so on. As for Muslims, their festivals (Eids) are associated with their religious rituals.  They have only two festivals or Eids:  Eid Al-Fitr (Celebration of the end of Ramadan) and Eid Al-Adha (festival of sacrifice).
When the Prophet, sallallaahu ‘alaihi wa sallam, came to Madinah and found the people celebrating two days he said:  “What are these occasions”?  They said: “We used to celebrate them in Jaahiliyya (before the coming of Islam)”.  He, sallallaahu ‘alaihi wa sallam, then said : “Allah has replaced them for you with the two better days (i.e. Eid Al-Fitr and Eid Al-Adha)”.  These two festivals which Allah prescribed to the Muslims are part of the rituals of Islam which should be commemorated and the purposes of which should be understood.
Rules pertaining to Eid:

1.  It is forbidden to fast on the day of both Eids, as it is understood from the hadith narrated by Abee Sa’eed that the Prophet, sallallaahu ‘alaihi wa sallam, forbade the fasting of the two Eids.
2.   It is recommended that both men and women observe Eid prayer in an open field as is clear in the hadith narrated by Um Atiya, may Allah be please with her, who said:  “We used to be ordered to come out on the day of Eid and even to bring the virgin girls from their houses and menstruating women so that they might stand behind the men and say takbir along with them and hope for the blessings of that day for purification from sins”.  Since menstruating women (who stay away from the musallah) as well as those who are virgin are commanded to observe Eid prayer, there is no doubt that the men, old and young are even strongly commanded to observe it.
3.  Eid prayer should be performed before the khutba of Eid as is confirmed in the hadith narrated by Ibn Amr, Abee Sa’eed, and Ibn Abbas, may Allah be pleased with them.
4.   It is recommended that the Imaam makes Takbeer (Allahu Akbar) during the prayer, seven times in the first Raka’at and five in the second.  This has been confirmed by the companions of the Salaf (our righteous predecessors).
5.   It is recommended that the Imaam recites in the first Raka’at Soorah Al-A’alaa (chapter 87) and Soorah Al-’Ghaashiah (chapter 88) in the second.  Other reports also show that the Prophet, sallallaahu ‘alaihi wa sallam, used to recite Soorah  Qaaf (chapter 50) and Soorah Al-Qamar (chapter 54) as is confirmed in Sahih Muslim.
6.  There is no Sunnah prayer either before or after Eid prayer as Ibn Abbas, may Allah,  be pleased with him, narrated that whenever the Prophet, sallallaahu ‘alaihi wa sallam, went for Eid prayer, he used to pray two Raka’at (of Eid) but nothing before or after them.
Article source: http://www.islamweb.net/emainpage/
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