“The Messenger of Allah, may Allah’s peace and blessings be upon him, would not perform anything before ‘Īd (prayer). However, when he returned to his home, he would perform two units of prayer (rak‘atayn).”

Narrated by Ibn Mājah (No. 1293), the wording is his; by al-Ḥākim in al-Mustadrak (No. 1102); and by al-Bayhaqī in al-Kubrā (No. 6228), from the ḥadīth of Abū Sa‘īd al-Khudrī, may Allah be pleased with him.
Authenticated in Ṣaḥīḥ al-Jāmi‘ (No. 4859) and Ṣaḥīḥ Ibn Mājah (No. 1069).

Brief Explanation of the Hadith

The companions, may Allah be pleased with them, transmitted the guidance of the Prophet, may Allah’s peace and blessings be upon him, to be followed. Among this is what they conveyed regarding the ‘Īd prayer. Abū Sa‘īd al-Khudrī, may Allah be pleased with him, reported that part of the Prophet’s, may Allah’s peace and blessings be upon him, practice in the ‘Īd prayer was that he did not perform any voluntary prayers before it, nor after it, in the musallā. Rather, when he came to the musallā, he would begin the ‘Īd prayer, and likewise, after completing the prayer and the sermon, he did not perform any voluntary prayers there. However, when he returned to his home, he would pray two rak‘ahs. This indicates the permissibility of performing voluntary prayer at home after completing the ‘Īd prayer, and that his, may Allah’s peace and blessings be upon him, omission of voluntary prayer applied only in the musallā.
It is derived from his, may Allah’s peace and blessings be upon him, practice that the default in acts of worship is imitation; wherever voluntary prayers before or after the ‘Īd prayer in the musallā were not transmitted from him, their omission constitutes the Sunnah.
In summary: the ‘Īd prayer is to be performed without any voluntary rak‘ahs before or after it. When a Muslim returns home, it is recommended to pray two rak‘ahs; if he prays more, there is no blame, for prayer is permissible at all times except during the prohibited periods.