General Rituals
Common greetings during this holiday are the Arabic greeting ‘Īd mubārak ("Blessed Eid") or ‘Īd sa‘īd ("Happy Eid"). In addition, many countries have their own greetings based on local language and traditions.
Typically, Muslims wake up relatively early in the morning—always before sunrise— offer Salatul Fajr, clean one's teeth with a Miswaak or a brush, take a shower (Gosul) after Fajr, put on new clothes or the best available, and apply perfume.
It is recommended to have a small breakfast (as a sign of not being on a fast on that day) of sweet dish preferably the date fruit, before attending the special Eid prayer (salah). It is a Sunnah that the Sadaqat-ul-fitr, an obligatory charity, is paid to the poor and the needy before performing the ‘Eid prayer by all those adult muslims who are required to pay Zakat. Muslims recite the following Takbir in the low voice while going to the Eid prayer: Allahu Akbar, Allahu Akbar, La ilaha ilal lahu wal Allahu Akbar, Allahu Akbar wa lilla hil hamnd. Another Sunnah of Prophet Muhammad (sas) is that Muslims should use two separate routes to and from the prayer ground (Idgah).

Eid prayer is performed in congregation in open areas like fields, squares etc or at mosques. No adhan or iqama (call) is to be pronounced for this Eid prayer, and it consists of only two rakaʿāt with additional 6 Takbirs. The Eid prayer is followed by the khutbah (sermon) and then a supplication (dua) asking for forgiveness, mercy and help for all living beings across the world. The khutbah also instructs Muslims as to the performance of rituals of Eid, such as the zakat. Listening to the khutbah of Eid is necessary (wajib) i.e. while the khutbah is being delivered, it is haraam to talk, walk about or offer prayer. It is then customary to embrace the persons sitting on either side of oneself, whilst greeting them. After the prayers, people visit their relatives, friends and acquaintances.
Source: wikipedia.org