Once Imam Abu Jafar al Baqir (as) asked his companions, Shall I show you how Prophet Mohammad (saww) used to Perform Ablutions?
[Narrator said] So we said: Yes!
Then a big bowl containing little water was brought and presented to the Imam (as). The Imam (as) then folded his sleeves and took a handful of water in his right hand and said: Remember! Only take water like this if your hands are pure. Then Imam (as)poured it onto his forehead while reciting Bismillah and spread that water around his beard and wiped his hand in the open area between the face and the forehead. Then Imam (as) took water in his left hand and poured water onto his right elbow and wiped it down with his hand so that water dropped out around the fingers of the Imam (as). The Imam (as) then took out some water using his right hand and poured onto his left elbow and wiped it with his right hand so that water dropped out around his fingers. This was followed by wiping the front of his head (from top to the end of hair line, upto forehead) with his right hand and then used both hands to wipe the surfaces of both feet using right hand for his right foot and left land for the left foot.

Note: For women it is obligatory to start washing their arms from inside.
Imam al Reza (as) said: Allah made it obligatory on the women, to begin the wudhu for the prayer from the underside of their arms and on the men from the upper side of their arms.¹
¹ [al Kafi, Volume no. 3, page no. 29]