'Urwa has narrated it on the authority of 'A'isha that when Messenger of Allah ﷺ took a bath because of sexual intercourse, he first washed his hands before dipping one of them into the basin, and then performed ablu- tion as is done for prayer. (Using translation from Muslim 316d)   

أَنَّ رَسُولَ اللهِ ﷺ كَانَ إِذَا اغْتَسَلَ مِنَ الْجَنَابَةِ بَدَأَ فَغَسَلَ يَدَيْهِ مِنَ الْإِنَاءِ قَبْلَ أَنْ يُدْخِلَ يَدَهُ فِي الْإِنَاءِ ثُمَّ تَوَضَّأَ مِثْلَ وَضُوئِهِ لِلصَّلَاةِ  

[Machine] The Messenger of Allah ﷺ performed ghusl to cleanse himself from major impurity. He washed his hands three times, then performed wudu for prayer. After that, he inserted his hand into a vessel of water and passed his fingers through the roots of his hair until it seemed to him that he had thoroughly cleaned his scalp. Then, he poured water onto his head, allowing it to flow over the rest of his body.  

أَنَّ رَسُولَ اللهِ ﷺ اغْتَسَلَ مِنَ الْجَنَابَةِ فَبَدَأَ فَغَسَلَ كَفَّيْهِ ثَلَاثًا ثُمَّ تَوَضَّأَ وُضُوءَهُ لِلصَّلَاةِ ثُمَّ أَدْخَلَ يَدَهُ فَخَلَّلَ بِهَا أُصُولَ شَعْرِهِ حَتَّى خُيِّلَ إِلِيَّ أَنَّهُ اسْتَبْرَأَ الْبَشَرَةَ ثُمَّ صَبَّ عَلَى رَأْسِهِ الْمَاءَ ثُمَّ أَفَاضَ عَلَى سَائِرِ جَسَدِهِ الْمَاءَ