There are many prophetic hadith on this topic. Here, we will mention just two of them, one describing his actions and other quoting his statements.
‘Abdullah ibn Ghanam related that Abu Musa al-Ash’ari gathered together his people saying, “O Tribe of Ash’ari, gather together, and gather your women and children to teach them how the Messenger of Allah, upon whom be peace, prayed with us in Madinah.” They all gathered to watch him perform ablution. After it, he waited until the sun had just passed the meridian and there was some shade, and then he made the azhan. He put the men in the row closest to him, the children in a row behind the men, and the women in a row behind the children. After the iqamah, he raised his hands and made the takbir, silently recited Surah al-Fatihah and another surah, repeated the takbir and bowed while saying, “Glory be to Allah and Praise be to Him” three times, after which he said, “Allah hears him who praises Him” and stood straight. He then made the takbir and prostrated, made another takbir, raised his head (and sat), repeated the takbir and prostrated again, after which he said the final takbir and stood up. In the first rak’ah he made six takbir, and he made another one when he stood for the second rak’ah. When he finished the prayer, he turned to his people and said, “Guard the number of my takbir and learn my bowings and prostrations, for this is how the Prophet prayed with us during this part of the day.” (Then he said) when the Prophet, upon whom be peace, finished the prayer, he turned toward the people and said, “O people, listen and understand. Allah has slaves who are neither prophets nor martyrs, but both the prophets and martyrs envy them for their closeness to Allah.” A bedouin stepped forward, pointed to the Messenger of Allah and said, “O Messenger of Allah, tell us about these people.” The Prophet was pleased with the bedouin’s request and said, “They are from various peoples and tribes who have no ties of relationship between them. They love each other purely for the sake of Allah. On the Day of Resurrection, Allah will present them pulpits of light for them to sit on. Their faces will be light and their clothes will be light. The people will be scared on the Day of Resurrection, but they will not be scared. They are the friends of Allah who will not have any fear upon them nor will they grieve.
As to the authenticity of this report, it is related by Ahmad and Abu Ya’la with a hassan chain. Al-Hakim says its chain is sahih.
Reported Abu Hurairah, “A man entered the mosque and, after praying, went to the Prophet, upon whom be peace. The Prophet, upon whom be peace, responded to his salutations and said, ‘Return and pray, for you have not prayed.’ This happened three times, and the man finally said, ‘By the One who sent you with the Truth, I do not know any better than that, so teach me.’ He said, ‘When you stand for the prayer, make the takbir and then recite what you can from the Qur’an. Then bow until you attain calmness and then come up again until you are standing straight. Then prostrate until you attain calmness in your sitting, and prostate until you attain calmness in your prostration. Do that during all of your prayer.” (Related by Ahmad, Muslim and al-Bukhari.)
These are general hadith that describe how the Prophet, upon whom be peace, prayed or what he said about its performance. Now we shall discuss those acts of the prayer which are obligatory and those which are sunnah.