The Messenger of Allah (peace and blessings be upon him) performed the prayer in its proper order, and in the hadith of Sayyiduna Malik bin al-Huwayrith (may Allah be pleased with him) he (peace and blessings be upon him) said: "Pray as you have seen me praying."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / Q3856
Sayyiduna Malik bin al-Huwayrith (may Allah be pleased with him) said that the Messenger of Allah (peace and blessings be upon him) said: "Pray as you have seen me praying. When the time of prayer comes, let one of you call the adhan, and then let the eldest of you lead the prayer."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 3856
It is reported from Sayyiduna Rifa'ah bin Rafi' (may Allah be pleased with him) that he was sitting with the Messenger of Allah (peace and blessings be upon him) in the mosque when a man entered the mosque and prayed. When he had completed the prayer, he greeted the Messenger of Allah (peace and blessings be upon him) and the other people with salam. He (peace and blessings be upon him) returned his greeting and said: "Go back and pray, for you have not prayed." He went and prayed again, and we began watching his prayer closely, but we could not see any fault in his prayer. When he had finished praying, he again came to the Messenger of Allah (peace and blessings be upon him), greeted him with salam, and greeted the people, and the Messenger of Allah (peace and blessings be upon him) said: "Go back and pray, for you have not prayed." He mentioned this twice or three times. Then the man said: O Messenger of Allah (peace and blessings be upon him)! I do not know what fault you find in my prayer. He (peace and blessings be upon him) said: "The prayer of none of you is complete until he performs ablution thoroughly as Allah has commanded him: he washes his face, washes his hands up to and including the elbows, and wipes his head and his feet up to the ankles. Then he says the takbir (when standing for the prayer), praises and glorifies Allah, and recites as much of the Qur'an as Allah permits him. Then he says the takbir and bows, placing his hands on his knees until all his joints settle in their places. Then he says 'Sami'a Allahu liman hamidah' (Allah has heard the one who praised Him) and stands up straight until every limb returns to its proper place. Then he straightens his back completely, then says the takbir and prostrates, placing his forehead firmly on the ground until his joints settle. Then, saying the takbir, he raises his head from the prostration, sits level on his seat and keeps his back straight."
Thus he described the prayer in this way until he finished, then said: "The prayer of none of you will be complete until he does this."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 3857