He had already prayed, then he called for water for purification. We said, "What is he going to do with it when he has already prayed? He only intends to teach us."A vessel containing water was brought, along with a basin. He poured from the vessel onto his hands and washed them three times. Then he rinsed his mouth and sniffed water into his nose three times from the same handful with which he took the water. Then he washed his face three times, washed his right arm three times and his left arm three times, wiped his head once, then washed his right foot three times and his left foot three times. Then he said, "Whoever wishes to know how the Messenger of Allah ﷺ performed ablution, this is it."
أخبرنا قتيبة قال حدثنا أبو عوانة عن خالد بن علقمة عن عبد خير قال أتينا
وقد صلى فدعا بطهور فقلنا ما يصنع به وقد صلى ما يريد إلا ليعلمنا فأتي بإناء فيه ماء وطست فأفرغ من الإناء على يديه فغسلها ثلاثا ثم تمضمض واستنشق ثلاثا من الكف الذي يأخذ به الماء ثم غسل وجهه ثلاثا وغسل يده اليمنى ثلاثا ويده الشمال ثلاثا ومسح برأسه مرة واحدة ثم غسل رجله اليمنى ثلاثا ورجله الشمال ثلاثا ثم قال من سره أن يعلم وضوء رسول الله ﷺ فهو هذا
Sahih, and Tirmidhi also narrated it in Kitab al-Tahara, chapter on what has been said about the wudu of the Prophet ﷺ and how it was, hadith (49), from the hadith of Abd Khayr as related here, and he said, hasan sahih. It is also found in Al-Kubra, hadith (77). See the previous hadith.