Putting aside the discussion on the actual origin of the Shi'i/Sunni split, Iran is predominantly Shi'a in large part due to the Safavids, the ruling dynasty in Persia from 1501–1736. They established Shi'i Islam as the state religion, and undertook significant efforts to ensure its spread throughout the empire. It has remained the predominant form in the area to today.

source: Brill's Encyclopaedia of Islam, 2nd Edition

This is not my field of study, however I'd like to help as best I can. Others that are more skilled in this field will hopefully follow up and flesh out what I've said (or tear it apart) – either way we'll get more discussion!

My background in this is based on research I've done in the past for multiple survey courses and modern imperial courses that I have taught.

In short, the split occurred over what I would call a religio-political (I'm reluctant to call it theocratic) schism in the 630s over who should inherit the highest level of authority in the Islamic faith. There were doctrinal/theological issues at stake over interpretations of the will and Hadith of Muhammad that sharpened this division. Again, there is much, much more to this, however I'd prefer to keep it brief in order to avoid overstepping my knowledge.

Regarding Iran being predominately Shia, /u/keyilan is correct in that it was largely a consequence of Safavid political power. It was a gradual change, and was not always violent. Much of the violence between Shia/Sunni followers can be attributed to political conflicts, particularly once we see the emergence of the predominately-Sunni Ottoman sultanate in the 14-16th centuries.

I'm reluctant to say that it is a direct comparison, but there are similarities in narrative and conflict to the Catholic/Orthodox split within Christianity. Questions of political (perhaps 'imperial') authority, when meshed with religious authority, interpretation and ambition, meshed to create the divisions and hostilities present in both faiths.

Sources: I have to say, one of my favorite go-to sources for broad topics like this are the 'Oxford History of x' line of books. You get multiple viewpoints, as well as concise narratives, and Oxford does a good job of filtering out junk publications (most of the time). The History of Islam is quite informative: http://www.oxfordislamicstudies.com/Public/book_ohi.html

You could combine it with the Oxford histories of the Ottomans and Persia for a truly comprehensive survey of the major historians, and historiography, of the topic.