The traditional narrative is, of course, yes, he was born in Mecca in 570 CE, the same year that an Ethiopian army containing an elephant besieged the city (Sura 105 The Elephant in its short few verses contains Muhammad relaying the message that God was not very pleased with the Ethiopian army termed "The Companions of the Elephant"). The traditional story involves Muhammad, the son of a lesser clan within the ruling Quraysh tribe, marrying Khadija, a rich merchant widow, and until the age of 40 in 610 Muhammad travelled up and down the Arabian peninsula and even into Syria on Khadija's business before the Angel Gibreel (Gabriel) commanded the illiterate merchant to read. After this incident, Muhammad founded a new faith and many disaffected people flocked to his banner before they were forced to flee to Yathrib, the city renamed Medina (New City) in 622 CE, whereupon Muhammad reconquered Mecca in 630 and died in 632.

I tend towards the traditional narrative barring the supernatural elements, myself, although in the last twenty years several prominent scholars have argued that Mecca was well off the beaten path and that, while Muhammad probably did actually use Medina as a staging ground, he was probably from Syria. I have many issues with this, but this version of the story has Muhammad born as a member of an Arab tribe in rural Syria, raised on Nestorian Christianity, and forming his own message, whereupon he moved to Medina. This new version of the story also challenges Muhammad's traditional death date, arguing that he at least lived long enough to lead the 634 assault on Byzantine Palestine.