Question: When does I’tikaaf begin?
Answer: The majority of the scholars state that I’tikaaf begins from the twenty first night  and not from Fajr on the twenty first day. Some of the Scholars state that it begins from Fajr on the twenty first day due to the hadeeth of Aa’isha (radiyallaahu ‘anhaa) in Bukhaaree which states:
“And when he had prayed Fajr, he entered his place of I’tikaaf.” (al-Bukhaaree no. 2041)
However the majority of the Scholars respond to that with the fact that the Messenger (salallaahu ‘alaihi wassallam) secluded himself from the people at Fajr – and as for the intention for I’tikaaf then that is from the beginning of the night because the last ten days begin from sunset on the twentieth. In Western custom: the twentieth night due to the fact that in Islamic tradition the night comes before its day.
Question: When does the person in I’tikaaf exit his I’tikaaf.? Is it after sunset on the night before ‘Eid or after Fajr on ‘Eid day?
Answer: The person in I’tikaaf comes out of his I’tikaaf when Ramadaan comes to an end, and Ramadaan comes to an end at sunset on the night before ‘Eid.
Source: Fataawa Fee Ahkaam as-Siyaam p. 501, of ‘Allaamah Muhammad Ibn Saalih Al-‘Uthaimeen (rahimahullaah).