Summary:
It is advisable to pray the Eid prayers in the open ground in congregation. If prayed in congregation the rules of "congregational prayers" should be followed. It is a 2 Rak-a't Salaat. Say Takbeeratul Ih'raam (Allahu Akbar). Make "Niyyat": "I Pray 2 Rak-a't Salaat ul Eid (Fit'r or Ad'haa), seeking nearness to Allah, in His obedience".
It is advisable to pray the Eid prayers in the open ground in congregation. If it prayed in congregation the rules of "congregational prayers" should be followed. It is a 2 Rak-a't Salaat. Say Takbeeratul Ih'raam (Allahu Akbar). Make "Niyyat": "I Pray 2 Rak-a't Salaat ul Eid (Fit'r or Ad'haa), seeking nearness to Allah, in His obedience".
First Rak-a't:
Recite Soorah Al Faatih'ah, and Soorah Al Aa'-laa and then Say Allaahu Akbar and Then recite the following Qunoot:
O Allah: You are the Lord of glory and greatness and the Lord of magnanimity and omnipotence and the Lord of pardon and mercy, and the worthiest of being feared and the Lord of forgiveness;
I beseech You in the name of this day, which You have decided to be feast for the Muslims, and to be safety and increasing honor for Muhammad—peace of Allah be upon him and his Household— (I beseech You) that You may send blessings upon Muhammad and the Household of Muhammad, and You may include me with every item of goodness with which You have included Muhammad and the Household of Muhammad, that You save me from any item of evil from which You have saved Muhammad and the Household of Muhammad, May Your blessings be upon him and upon them. O Allah: I pray You for the best of all that for which Your righteous servants have prayed You, and I seek Your protection against all that against which Your righteous servants have asked Your protection. [1]
(Please remember that the above noted and have to be rcited, one after the other, 5 times).
Then say the 6th Takbeer and perform Rukoo and Sujood of the first Rak-a't. Second Rak-a't: Recite Soorah Al Faatih'ah, and Soorah Ash-Shams and then Say Takbeer (Allahu Akbar) and Qunoot 4 times, one after the other.
Note:
1. اللهم اهل الكبرياء و العظمة و اهل الجود والجبروت و اهل العفو والرحمة و اهل التقوي والمغفرة اسئلك بحق هذا اليوم الذي جعلته للمسلين عيدا و لمحمد صلي الله عليه و آله ذخرا و مزيدا ان تصلي علي محمد و ال محمد و ان تدخلني في كل خير ادخلت فيه محمدا و ال محمد و ان تخرجني من كل سوء اخرجت منه محمدا و ال محمد صلواتك عليه و عليهم اللهم اني اسئلك خير ما سئلك عبادك الصالحون و اعوذ بك مما استعاذ منه عبادك الصالحون
Source: http://english.tebyan.net/newindex.aspx?pid=49674&Keyword=+Eid+Al-Fitr