How did the Prophet (ﷺ) performed ghusl?

• The Prophet (ﷺ) began his ghusl by washing his hands and genitals.[1]
• Then he (ﷺ) poured water with his right hand and washed his genitals with his left hand.[2]
• After washing the genitals, the left hand should be cleaned with soap before proceeding. Earth was used to clean away the impurities.[3]
• He (ﷺ) would make wudhu.[4]
• Following that he (ﷺ) would rub water into the roots of his hair and then wash his head.[5]
• Washing the Body: Then he (ﷺ) would pour water over his whole body. [6]
• Washing the Feet: Sometimes he (ﷺ) would leave the washing of his feet until the end of his ghusl.[7]

Note: When bathing using soap, one may complete the soaping and washing of the whole body including the hair, then proceed to make wudhu and the complete wash. The wash may be under a shower, however, it should not be in a tub of standing water, because one will be washing with unclean water. Abu Hurayrah (رضى الله عنه) quoted the Prophet (ﷺ) as saying,

"None of you should bathe in standing water when in a state of sexual defilement."[8]  

References:

[1]  ‘Aa'ishah (رضى الله عنها) reported that whenever the Prophet (ﷺ) wanted to take a ghusl due to sexual defilement (janaabah), he (ﷺ) first washed both hands [three times]. (Sahih Muslim vol.1, p.183,no. 618)

[2] (Sahih Muslim vol.1, p.182-3,no. 616 & Sunan Abu Dawud, vol.1,p.61, no. 242)

[3] Maymoonah (رضى الله عنها) said, "I placed water near Allah’s Messenger (ﷺ) to take a bath following sexual intercourse. He (ﷺ) washed his palms twice or thrice and then put his hand in the basin and poured water over his genitals and washed them with his left hand. He (ﷺ) then placed his hand on the ground and rubbed it forcefully..." (Sahih Muslim vol.1, p.183,no. 620)

[4] ‘Urwah (رضى الله عنه) related from ‘Aa'ishah (رضى الله عنها) that when the Messenger of Allah (ﷺ) took a bath because of sexual defilement, he (ﷺ) first washed his hands before dipping them in the basin, and then performed wudhu like his wudhu for formal prayer. (Sahih Muslim vol.1, p.183,no. 619)

[5] ‘Aa'ishah (رضى الله عنها) reported that whenever the Messenger of Allah (ﷺ) bathed due to sexual intercourse...he (ﷺ) took some water and rubbed it with his fingers into the roots of his hair. Then he (ﷺ) poured three handfuls of water on his head. (Sahih Muslim vol.1, p.182-3, no. 616)

‘Aa'ishah (رضى الله عنها) also related that he (ﷺ) took a handful of water from the basin and washed the right side of his head first, then the left, then he (ﷺ) took a handful and poured it on his head. (Sahih Muslim vol.1, p.183, no. 623).

[6] ‘Aa'ishah (رضى الله عنها)  narrated that whenever Allah’s Messenger (ﷺ) took a ghusl due to sexual intercourse, ...he (ﷺ) would pour three handfuls of water over his head and then pour water over all of his body. (Sahih Al- Bukhari, vol.1, p. 157, no. 248, Sahih Muslim vol.1, p.182-3,no. 616 & Sunan Abu Dawud, vol.1,p.61, no. 242)

[7] Maymoonah (رضى الله عنها) was quoted as saying, "Allah’s Messenger (ﷺ) made wudhu like that for prayer but he (ﷺ) did not wash his feet. He (ﷺ) then washed his genitals and the parts of his body on which there was discharge. Then he (ﷺ) poured water over himself, stepped away from where he (ﷺ) was standing and washed his feet. This is how he (ﷺ) took a ghusl due to sexual defilement." (Sahih Al- Bukhari, vol.1, p. 157, no. 248, & Sunan Abu Dawud, vol.1, p.61, no. 245).

[8] (Sahih Muslim vol.1, p.168,no. 556.)