1- Fasting: It is haram to fast on the days of Eid because of the hadith of Abu Sa`id Al-Khudri (may Allah be pleased with him) in which he said that the Messenger of Allah (peace and blessings be upon him) forbade fasting on the day of Fitr and the day of Adha. (Muslim)
2- Offering Eid Prayers: Some of the scholars say that Eid prayers are obligatory – this is the view of the Hanafi scholars and of Ibn Taymiyyah. Some scholars say that Eid prayer is Fard Kifayah (a communal duty, binding on the Muslims as a group, and it is fulfilled if a sufficient number of people perform it, thereby absolving the rest of sin). This is the view of the Hanbalis. A third group says that Eid Prayer is Sunnah Mu’akkadah (confirmed sunnah). This is the view of the Malikis and Shafi`is.
3- Offering Supererogatory Prayers: There are no Supererogatory Prayers to be offered either before or after the Eid Prayer, as Ibn `Abbas reported that the Prophet (peace and blessings be upon him) used to come out on the day of Eid and pray two rak`ahs, with nothing before or after them. This is the case if the Prayer is offered in an open area. If however, the people pray the Eid Prayer in a mosque, then they should pray two rak`ahs for Tahiyat Al-Masjid.
4- Women attending the Eid Prayers: According to the Sunnah of the Prophet (peace and blessings be upon him), everyone is urged to attend Eid prayer, and to co-operate with one another in righteousness and piety. The menstruating woman should not forsake the remembrance of Allah or places of goodness such as gatherings for the purpose of seeking knowledge and remembering Allah – apart from mosques. Women, undoubtedly, should not go out without the Hijab.