What year was Jesus born?
We don't know. The current calendar is based on calculations that place the birth of Jesus in the year 1 A.D. At that time events were normally recorded by what year they happened in someone's reign. Thus something that happened six years into Caesar John's reign would be rendered "such and such happened in the sixth year of the reign of Caesar John." The monk Dionysius Exiguus began the practice of recording events according to the Incarnation, Anno Domini, "in the year of our Lord." How exactly he arrived at that date we do not know. However, modern theologians and historians have debated the accuracy of that calculation and argue that Jesus was born anywhere from 6 B.C. to A.D. 6.
If we date the birth of Jesus from the reign of Herod, we would see that Herod died in 4 B.C. So, depending upon how soon after the visit of the Magi Herod died, we get a date around 7 or 6 B.C. for the birth of Jesus. There is still debate about exactly when Herod died so depending on which date is acceptable the answer could be anywhere from 6 B.C. to 1 B.C.
Luke tells us that Jesus was about thirty years old when he began his public ministry (Luke 3:23). Luke also tells us that John the Baptist began his ministry in the fifteenth year of Tiberius Caesar (3:1), which would be approximately the year 29 A.D. That places that birth of Jesus around 3 B.C. to 2 B.C.
If we try to base the birth of Jesus on the appearance of the star that the Magi followed, we end up with different dates based on what we think the star might have been. If it was a particular alignment of the Earth lapping Jupiter, we are in 6 B.C. If it was the alignment of Jupiter with Venus, we are in 3 B.C. to 2 B.C. If it was a comet, we are looking at 6 B.C. to 5 B.C. If it was the triple conjunction of Jupiter, Venus, and the star Regulus, we are in the year 2 B.C.