The Order to Perform Wudu
Allah said
When you stand for (intend to offer) the Salah,
Allah commanded performing Wudu' for the prayer. This is a command of obligation in the case of impurity, and in the case of purity, it is merely a recommendation.
It was said that in the beginning of Islam, Muslims had to perform Wudu' for every prayer, but later on, this ruling was abrogated.
Hadith
Imam Ahmad bin Hanbal recorded that Sulayman bin Buraydah said that his father said, "The Prophet used to perform Wudu' before every prayer. On the Day of Victory, he performed Wudu' and wiped on his Khuffs and prayed the five prayers with one Wudu'. `Umar said to him, `O Messenger of Allah! You did something new that you never did before.' The Prophet said,
The Prophet of Allah said
"I did that intentionally O 'Umar"
Muslim and the collectors of the Sunan also recorded this Hadith. At-Tirmidhi said,"Hasan Sahih." Ibn Jarir recorded that Al-Fadl bin Al-Mubashshir said, "I saw Jabir bin `Abdullah perform several prayers with only one Wudu'. When he would answer the call of nature, he performed Wudu' and wiped the top of his Khuffs with his wet hand. I said, `O Abu `Abdullah! Do you do this according to your own opinion' He said, `Rather, I saw the Prophet do the same thing. So, I do what I saw the Messenger of Allah ﷺ doing."' Ibn Majah also recorded this Hadith.
Ahmad recorded that `Ubaydullah bin `Abdullah bin `Umar was asked; "Did you see `Abdullah bin `Umar perform Wudu' for every prayer, whether he was in a state of purity or not," So he replied, "Asma' bint Zayd bin Al-Khattab told him that `Abdullah bin Hanzalah bin Abi `Amir Al-Ghasil told her that the Messenger of Allah ﷺ was earlier commanded to perform Wudu' for every prayer, whether he needed it or not. When that became hard on him, he was commanded to use Siwak for every prayer, and to perform Wudu' when Hadath (impurity) occurs.
`Abdullah (Ibn `Umar) thought that he was able to do that (perform Wudu' for every prayer) and he kept doing that until he died." Abu Dawud also collected this narration. This practice by Ibn `Umar demonstrates that it is encouraged, not obligatory, to perform Wudu' for every prayer, and this is also the opinion of the majority of scholars. Abu Dawud recorded that `Abdullah bin `Abbas said that when the Messenger of Allah ﷺ once left the area where he answered the call of nature, he was brought something to eat. They said, "Should we bring you your water for Wudu" He said,
I was commanded to perform Wudu' when I stand up for prayer.
Wudu' is only commanded when standing up for prayer
At-Tirmidhi and An-Nasa'i also recorded this Hadith and At-Tirmidhi said, "This Hadith is Hasan." Muslim recorded that Ibn `Abbas said, "We were with the Prophet when he went to answer the call of nature and when he came back, he was brought some food. He was asked, `O Messenger of Allah! Do you want to perform Wudu" He said,
Why? Am I about to pray so that I have to make Wudu?
The Intention and Mentioning of Allah's Name for Wudu
Allah said
(then wash your faces...)
The obligation for the intention before Wudu' is proven by this Ayah;
When you stand (intend) to offer the Salah then wash your faces...
This is because it is just like the Arabs saying; "When you see the leader, then stand."
Hadith
Recorded in Two Sahihs
Actions are judged by their intentions, and each person will earn what he intended.
It is also recommended before washing the face that one mentions Allah's Name for the Wudu'
A Hadith that was narrated by several Companions states that the Prophet said,
There is no Wudu' for he who does not mention Allah's Name over it.
It is also recommended that one washes his hands before he puts his hands in the vessel of water, especially after one wakes up from sleep,
As recorded in the Two Sahihs that Abu Hurayrah said that the Messenger of Allah ﷺ said,
If one of you wakes up from his sleep, let him not put his hand in the pot until he washes it thrice, for one of you does not know where his hand spent the night.
The face according to the scholars of Fiqh starts where the hair line on the head starts, regardless of one's lack or abundance of hair, until the end of the cheeks and chin, and from ear to ear.
Statement in regards to passing the fingers through the beard while perfuming wudu
Imam Ahmad recorded that Abu Wa'il said, "I saw `Uthman when he was performing Wudu... When he washed his face, he passed his fingers through his beard three times. He said, `I saw the Messenger of Allah ﷺ do what you saw me doing. At-Tirmidhi and Ibn Majah also recorded this Hadith. At-Tirmidhi said \"Hasan Sahih.\" while Al-Bukhari graded it Hasan.
How to Perform Wudu