It was narrated from 'Amr bin Yahya Al-Mazini that his father said to 'Abdullah bin Zaid bin 'Asim - who was one of the Companions of the Prophet (ﷺ) and the grandfather of 'Amr bin Yahya:
Can you show me how the Messenger of Allah (ﷺ) used to perform Wudu'? 'Abdullah bin Zaid said: Yes. He called for (water for) Wudu' and poured some onto his hand, washing each hand twice. Then he rinsed his mouth and nose three times, then he washed his face three times, then he washed each hand twice, up to the elbow. Then he wiped his head with his hands, back and forth, starting at the front of his head and moving his hands to the nape of his neck, then bringing them back to the place he started. Then he washed his feet.