This post title is one of the most important questions in the study of Christian origins. Based on the evidence available to us, Jesus never claimed to be God and pointed others to the coming kingdom of the one, true God of Israel. So when and how did he himself come to be worshiped by many of his followers after his death.
Larry Hurtado's Lord Jesus Christ: Devotion to Jesus in Earliest Christianity provides one model for consideration. The just released volume by James D. G. Dunn, Beginning From Jerusalem, also provides extensive analysis of the question (more on both of these substantial works in later posts).
Another way into the subject, requiring less of an investment in time and money, is to be found at April DeConick's blog site, where yesterday she began a series: Creating Jesus: How Jesus Became God. You will be well served to keep up with April's look at Christology and what Dunn calls "Christianity in the making."