Muhammad was born in Mecca approximately 570 C.E. and was a member of the Quraysh tribe. As with Moses and Jesus, we know little about his childhood. His parents died when he was young, and he never learned to read or write. When he was 12, he visited Syria and had his first exposure to Jews and Christians and apparently developed a respect for these "People of the Book." At 25, Muhammad married a widow named Khadija who was involved in trade and got him involved in it as well.
During one trading journey when he was about 40, Muhammad had an encounter with the angel Gabriel revealed to him special revelations. Different opinions exist on whether Mohammed miraculously read or just repeated the revelations, which said he was to become the messenger of God. Following his prophetic experience, Mohammed returned to his wife and began spreading the teachings he learned.
Afterward, Muhammad began to develop a code of behavior that he said had come from Allah, or God. Some of the revelations included that the world would end, that God would judge humans mercifully if they submitted to His will, and that people should pray to show their gratitude to God.
The people who accepted Muhammad's teachings came to be known as Muslims and their religion Islam, Arabic for "surrender [to the will of Allah]." Muhammad was regarded as the last and most perfect prophet. During the two centuries after Muhammad's death, the laws of Islam were codified in the Shariah, and Muhammad was regarded as the last and most perfect prophet. The word of God was revealed to him through the angel Gabriel and recorded in the Arabic language in the Koran (or Qur’an).
The principles of Islam were developed over time and, as was the case with earlier men professing to be prophets, not everyone was willing to accept Muhammad's claim to be God's messenger. Muhammad was attacking the way of life of the more powerful families in the Quraysh tribe, and they were not happy about it. In addition to having to persevere the criticism of his views, he also suffered terribly when his wife and uncle died in the same year.
In 622, Muhammad left Mecca for an oasis then known as Yathrib. This trip became known as the hejira, the flight from persecution in Mecca. The term has also come to mean leaving a pagan community for one that adheres to the laws of Islam. In his new home, which was later renamed Medina, Muhammad became a mediator, arbitrating disputes between tribes.
Interestingly, Medina also had a sizeable Jewish community, which had probably moved there after being expelled from Palestine by the Romans. Muhammad respected the Jews, and his early teachings appeared to borrow from Jewish tradition. The Jews began to distance themselves from Muhammad, however, when he became critical of their not recognizing him as a prophet.
Once it was clear the Jews would not accept him, Muhammad began to minimize or eliminate the Jewish influence on his beliefs. For example, he shifted the direction of prayers from Jerusalem to Mecca, made Friday his special day of prayer, and renounced the Jewish dietary laws (except for the prohibition on eating pork). Originally, he said the Arabs were descendants of Abraham through his son Ishmael, but in the Koran Abraham's connection to the Jews is denied, with Muhammad asserting that Abraham is only the patriarch of Islam, not Judaism as well, because he "surrendered himself to Allah."
One of the immediate consequences of Muhammad's frustration was the expulsion of two Jewish tribes from Medina and the murder of all the members of a third Jewish tribe (except for the women and children, who were sold into slavery). But even worse for the long-term treatment of the Jews were a number of inflammatory statements about Jews that Muhammad made that appear in the Koran — which, over the years, stoked Arab/Islamic anti-Semitism.
Muhammad slowly began to build his power base both by the persuasiveness of his faith and the old-fashioned way: by marrying women from important families to gain political advantage. He came to control the oases and markets, which forced other traders and tribesmen to negotiate with him. When he finally returned to Mecca, it was at the head of an imposing army that forced the residents to capitulate.
Muhammad died in 632, and it was left to his followers to carry on the traditions he had begun. His followers developed Islam, just as the followers of Moses and Jesus developed Judaism and Christianity over time.
Sources: Bard, Mitchell G. The Complete Idiot's Guide to Middle East Conflict. 3rd Edition. NY: Alpha Books, 2005.