Mishkat al-Masabih 435

ʿĀʾisha, the Prophet’s wife, reported that when the Prophet performed the full ritual bath after sexual impurity, he began by washing his hands. Then he performed ablution as for prayer, inserted his fingers into the water and worked them through the roots of his hair, poured three handfuls of water over his head with both hands, and then poured water over his entire body.

In a version transmitted by Muslim, he first washed his hands before putting them into the vessel. Then he poured water from his right hand onto his left, washed his private parts, and performed ablution.