The Messenger of God(swt) during the first days of His Holy Prophecy, when according to the text of The Holy Koran, was commanded by God to invite his closer relatives to come to His religion, of Islam. 

He told them very clearly that whoever would be the first to accept His invitation would then become his Sole Successor, his Calipha and his Inheritor, after his death. 

Ali Ibin Abe Taleb(as) then a small boy of about twelve years of age, was the first and only one to readily step forth and embrace unconditionaly Islam. The Prophet(pbuh&hf) accepted Ali's submission to the Faith and thus fulfilled his promise. 

From the Shi'ite point of view it appears as unlikely that the Leader of a new and important movement, during the first days of his activity, should introduce to strangers, or one of his associates as his Successor and Deputy but not introduce him to his completely loyal and devout aides and friends. 

Nor does it appear likely that such a Leader should accept someone as his deputy and successor and introduce him to others as such, but then throughout his life and religious call deprive his deputy of his duties as deputy, disregard the respect due to his position as the appointed successor, and refuse to make any distinctions between him and others. 

The Prophet(pbuh&hf), according to many unquestioned and completely authenticated Hadeeths, both Sunni and Shi'ite, clearly asserted that Ali was infallible of any wrong doings and sin in all his actions and sayings. 

Whatever he said and did was perfect and true in every conformity with the teachings of the religion, and he was noteablly undisputedly the most knowledgeable of all men on the face of the earth, in all matters pertaining to the Islamic sciences and injunctions. 

During the period of the Prophecy Ali performed valuable services and made untold remarkable sacrifices. When the infidels of Mecca decided to kill The Prophet(pbuh&hf) and surrounded his house. The Holy Prophet(pbuh&hf) decided that it would be wise to emigrate to Medina. He turned only to Ali for help, and asked him, 

"Will you sleep in my bed at night, 
so that they will think that I am asleep, 
and I will be secure from being pursued by them?"

Hence the extraordinary Migration of the Muslims from Mecca to Yathrib marks the very date of origin of the Islamic Calendar, known as the Hijrah, simply transalted meaning the Migration. 

Ali also served Islam 
By fighting courageousily in the battles of: 

1. Badr 
2. Uhud 
3. Khaybar 
4. Khandaq 
5. Hunayn 

For the Shia 
The central evidence of Ali's legitimacy as the sole successor to The Prophet(pbuh&hf) is in the event of Ghadeer Khumm, when The Holy Prophet(pbuh&hf) chosed Ali Ibin Abe Taleb(as) above all else, to The 'General Guardianship' or (Waldyat Al-Imamah) of the people, and made Ali, like himself, 'their Guardian' or (Wali). 

It is obvious that because of such distinctive services and recognition, because of Ali's special virtues which were acclaimed by all, and because of the great love The Prophet showed for him. As well as some of the Companions of The Prophet(pbuh&hf) who knew Ali Ibin Abe Taleb(as) also well, and who were also champions of virtue and truth, came to love Ali too. 

They all assembled around Ali and followed him to such an extent that many others began to consider their love for him to be much too excessive and a few perhaps also became very jealous of him and of his great virtious ways. 

Besides all these Elements 
We see in the many Ahdeeths or Sayings of The Holy Prophet Al-Mustafa(pbuh&hf) reference to the "Shia of Ali" and to the "Shia of The Infallible Ahlu Bayt(as), or The Holy Household of The Prophet Mohammad(pbuh&hf)".