The
first fitnah took place in the wake of the initial
conquering/
expansion phase of the
caliphate and Islamic society in general. A group of
soldiers, primarily composed of those who had
conquered
Egypt, were
convinced by
Umayyad associates of the
caliph 'Uthman that if they would simply come to
Medina to negotiate, 'Uthman would
redress the wrongs that they felt had been done to them. (They felt that although they had done most of the fighting in Egypt they were recieving an
unfairly
small amount of the
booty and
spoils.) Negotiations turned
sour when the soldiers discovered that their leaders were actually going to be
executed when they arrived, and some of the
dissatisfied soldiers called on 'Uthman to
abdicate the caliphate. He responded, "I would never take off a
garment with which
God has clothed me." The soldiers became
mutinous and broke into the caliph's house and killed him.
With the former caliph dead under controversial circumstances, the man to follow him would certainly not have an easy time of ruling. That man wound up being 'Ali, the nephew of the prophet Muhammad and husband of the prophet's only child. 'Ali was supported mostly by those parties that had opposed 'Uthman and was opposed by those who had supported 'Uthman, including the prophet's favorite wife A'ishah. It was not long before hostilities erupted into violence. In 656 CE, the opposing forces fought at the Battle of the Camel. 'Ali's forces won and he was generally recognized as caliph, ruling from the former military garrison of Kufah.
Unfortunately, things were not to be that easy for either the new caliph or the society that he ruled. Mu'awiyah, 'Uthman's governor of Syria, was a very powerful man who opposed 'Ali still. He called for vengeance for the killing of 'Uthman and continued the rebellion against 'Ali. 'Ali's army met the army of Mu'awiyah at the battle of Siffin, which wound up being a stalemate. The two parties then tried to solve the problem through arbitration, which unfortunately accomplished nothing as far as the war's end was concerned. A large number of 'Ali's men felt that he was not representing them as well as they would like, though, and split with his group to become the Kharijis, an ultra-extreme faction that believed that all the rest of the world was a legitimate target for jihad. The Kharijis were defeated at their first battle with 'Ali's forces at an Iraqi canal, but they managed to exist for several hundred more years, playing an important part in many aspects of Islamic history, an example of which we'll see shortly.
With 'Ali's attention necessarily divided between the Kharijis and the rebelling Syrian forces, Mu'awiyah felt secure enough to claim the caliphate for himself, especially since he had conquered Egypt while 'Ali was occupied with the Kharijis. He declared himself caliph in 660 and began to rule the Islamic world from Jerusalem. 'Ali, meanwhile, was still alive and claiming to be the caliph from Kufah. This conflict of interests was short-lived, however, as 'Ali was assassinated by a Khariji by the name of Ibn-Muljam in 661. 'Ali's first son was not as enthusiastic about inheriting such a difficult job as his father had been, so he sold his rights to the caliphate to Mu'awiyah and never showed his face in politics again.
Mu'awiyah wound up being the last man standing and so got the caliphate. The first fitnah lasted from 656 to 661, but its historic echoes can be felt even today. 'Ali's supporters became the Shi'is, or party of the prophet's family, while the rest of the world became the Sunnis. These two factions still constitute almost the only major sects within Islam to this very day. The Kharijis played a major part at many points later in Islamic history, although their aforementioned extreme inability to get along with others extinguished them after about 200 years of existence.
Virtually all information in this writeup is taken from Marshall G. S. Hodgson's The Venture of Islam, v.1, The Classical Age of Islam. Some of it, however, is remembered from lectures by professor Wadad Kadi.