It's interesting that research continues to be done on this. Usually Jesus' birth is placed by Herod the Great's death, which was set by Josephus in 4 BC. But I recently read an article by John Cramer (Professor of Physics, Oglethorpe University, Atlanta GA) that argues:

"The standard date of Herod’s death is based on Josephus’ remark in Antiquities 17.6.4 that there was a lunar eclipse shortly before Herod died. This is traditionally ascribed to the eclipse of March 13, 4 BC. Unfortunately, this eclipse was visible only very late that night in Judea and was additionally a minor and only partial eclipse.
There were no lunar eclipses visible in Judea thereafter until two occurred in the year 1 BC. Of these two, the one on December 29, just two days before the change of eras, gets my vote since it was the one most likely to be seen and remembered. That then dates the death of Herod the Great into the first year of the current era, four years after the usual date.
Perhaps the much-maligned monk who calculated the change of era was not quite to far off as has been supposed."

Just as a note of trivia, there was no 0-year. The creators of the calendar jump from 1 BC to AD 1.

Most people now believe Jesus was born in about 6 BC, give or take. It could have been anywhere from 5-7 BC. (The creators of the Julian calendar, that we use, and base our AD and BC on, were wrong in their calculations.) And Jesus was almost certainly born in the fall, most likely around Sukkot (the Feast of Tabernacles). The shepherds were out in the field, keeping watch over their flocks by night, and that is most likely a spring or fall scenario in Bethlehem.

We celebrate on December 25 because that's when the winter solstice is. Most Christmas traditions say that the early Romans always had celebrations at the winter solstice, so the Christians decided to get in on the deal and celebrate Christmas then, because they could get away with it. And it stuck. Now, millennia later, we still celebrate on Dec. 25. The Russians, however, celebrate Christmas on January 5 or 6. In any case, Jesus was most likely born in the fall in 5 or 6 BC. It most certainly was not 3 AD. Herod the Great, who tried to kill the baby Jesus by sending soldiers to Bethlehem to slaughter all the babies, died in 4 BC, so Jesus was born before that, and was probably younger than 2 at the time.

It has nothing to do with translation.

(There is a fascinating possible connection between Jesus's birth and Sukkot—the Feast of the Ingathering of the Harvest. If it's true, he might have been conceived by the Holy Spirit on Hanukkah [the Light of the World], six months after John the Baptist was conceived, which may have been on Passover. Nine months later Jesus is born on the first day of Sukkot [perhaps even in a tent erected for the occasion], the Feast of Tabernacles (see John 1.14). The tent symbolized their slavery in Egypt, and here Jesus is born in the most humble of stations. Sukkot also commemorates the Exodus—the freeing of the people from slavery.

Sukkot might also help to explain why there was no room in any inns—the city and even the small towns were swollen with pilgrims. Psalm 118.25 was the traditional reading: "Blessed is he who comes in the name of the Lord."

If this is so, then Jesus might have been born on the first day of Sukkot and circumcised on the last day of the 8-day festival, Shemini Atzeret—a day of celebration and joy [here the child of the covenant, Jesus, marked with the sign of the covenant, circumcision]—the time of slavery is over, and the day of freedom has come!

My professor told us that Jesus was born in the year 3 AD, but I thought that He was born in 0, hence BC and AD? Also, he told us that Jesus was born in March but because of translation we all think it was during Christmas time?