Praise be to Allah
Firstly:
al-Bukhaari (1041) and Muslim (911) narrated that Abu Mas‘ood al-Ansaari (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “The sun and the moon are two of the signs of Allah by means of which Allah creates fear in His slaves. They do not become eclipsed for the death of any person. If you see anything happen to them, then pray and call upon Allah until you are relieved of that.”
Al-Bukhaari (1059) and Muslim (912) narrated that Abu Moosa (may Allah be pleased with him) said: The sun was eclipsed, and the Prophet (blessings and peace of Allah be upon him) got up in a state of anxiety, thinking that it was the Hour. He came to the mosque and began to pray, standing, bowing and prostrating for the longest time I ever saw him do, and he said: “These signs that are sent do not occur for the death or birth of anyone, rather Allah sends them to create fear in His slaves. If you see any of them, then hasten to remember Him, call upon Him and ask Him for forgiveness.”
Secondly:
The way in which the eclipse prayer is performed is as follows:
The worshipper recites the opening takbeer (takbeerat al-ihram) and the opening supplication (du‘aa’ al-istiftaah), then he seeks refuge with Allah.
Then he recites al-Faatihah, followed by a lengthy recitation.
Then he bows, making it lengthy.
Then he rises from bowing and says: Sami‘a Allahu liman hamidah, Rabbana wa laka al-hamd (Allah hears those who call upon him; our Lord, to You be praise).
Then he recites al-Faatihah again, followed by another lengthy recitation but it is not as long as the first recitation.
Then he bows again, making it lengthy but not as long as the first time.
Then he rises from bowing and says: Sami‘a Allahu liman hamidah, Rabbana wa laka al-hamd (Allah hears those who call upon him; our Lord, to You be praise), and stands for a long time.
Then he prostrates twice, making each prostration lengthy, and sits for a long time between the two prostrations.
Then he gets up for the second rak‘ah, and does the same as he did in the first rak‘ah, bowing twice and so on, but each action is not as long as in the first. Then he recites the tashahhud and the tasleem.
See al-Mughni by Ibn Qudaamah (3/323); al-Majmoo‘ by an-Nawawi (5/48).
This is indicated by the hadith of ‘Aa’ishah. Al-Bukhaari (1046) and Muslim (2129) narrated that ‘Aa’ishah, the wife of the Prophet (blessings and peace of Allah be upon him) said: The sun was eclipsed during the lifetime of the Messenger of Allah (blessings and peace of Allah be upon him). The Messenger of Allah (blessings and peace of Allah be upon him) went out to the mosque and stood and said takbeer, and the people formed rows behind him. The Messenger of Allah (blessings and peace of Allah be upon him) recited for a long time, then he said takbeer and bowed for a long time. Then he said, “Sami‘a Allahu liman hamidah (Allah hears those who praise Him).”
Then he stood and did not prostrate, and recited for a long time, but it was shorter than the first time.
Then he said takbeer and bowed for a long time, but it was shorter than the first time.
Then he said, “Sami‘a Allahu liman hamidah, Rabbana wa laka al-hamd (Allah hears those who call upon him; our Lord, to You be praise).”
Then he prostrated. Then he did likewise in the second rak’ah.
Thus he did four bowings and four prostrations.
And Allah knows best.