This is how the Messenger of Allah (may Allah's peace and blessings be upon him) performed ablution
Authentic hadithعن عبْدِ خيْرٍقال: أتانا علي رضي الله عنه وقد صلَّى فدعا بطَهور، فقلنا ما يصنع بالطَّهور وقد صلَّى ما يُريد، إلا ليعلِّمَنا، فأُتِي بإناء فيه ماء وطَسْت، فأفْرَغَ من الإناء على يمينه، فغسل يديه ثلاثا، ثم تَمَضْمَضَ واسْتَنْثَر ثلاثا، فمَضْمَض ونَثَرَ من الكفِّ الذي يأخُذ فِيه، ثم غسل وجهه ثلاثا، ثم غسل يده اليمنى ثلاثا، وغسل يده الشِّمال ثلاثا، ثم جعل يده في الإناء فمسَحَ بِرأسه مرَّة واحدة، ثم غسل رجله اليمنى ثلاثا، ورِجْلَه الشمال ثلاثا. ثم قال: «مَنْ سرَّه أن يعْلَم وُضُوء رسول الله صلى الله عليه وسلم فهو هذا».
‘Abd Khayr reported: ‘Ali ibn Abi Tālib (may Allah be pleased with him) came to us after he had prayed. He asked for water and we said: "What is he going to do with the water as he has (already) prayed? He only wants to teach us." A container of water and a basin were brought to him. He poured some water onto his right hand and washed his hands three times. Then he rinsed his mouth and nose three times, using the hand with which he took the water. Then he washed his face three times and he washed his right arm three times and his left arm three times. Then he put his hand in the container and wiped his head once. Then he washed his right foot three times and his left foot three times. Then he said: 'Whoever wanted to learn how the Messenger of Allah (may Allah's peace and blessings be upon him) performed ablution, this is it.
Explanation
This Hadīth describes the ablution of the Prophet (may Allah's peace and blessings be upon him). ‘Abd Khayr related that ‘Ali (may Allah be pleased with him) went to them after he had prayed. He asked them for water to perform ablution. At first they were surprised by this, as he had already prayed, but then realized that he wanted to teach them how the Prophet (may Allah's peace and blessings be upon him) used to perform ablution. They brought the water and he poured some of the water onto his right hand and washed both of his hands three times. He then he rinsed his mouth and washed his nose three times using the same hand that he had taken the water with. He then washed his face three times. The limits of the face are from the normal hair line at the top of the forehead to the end of the chin, including the upper part of the beard, and from one ear to the other. He then washed his right then left arm three times, including the elbows. He wiped over his head only once. Lastly, he washed his right and then left foot three times. He said that this was the way the Prophet (may Allah's peace and blessings be upon him) performed ablution.
Source · Narrated by Ibn Majah - An-Nasaa’i - Narrated by Abu Daoud - Narrated by Ahmad
From the Hadith Encyclopedia (hadeethenc.com).