How did the writers of the New Testament know the details of the birth of Jesus?

The question assumes that they actually did know the details and they didn’t make them up.

I am not a Biblical scholar, but I believe Luke learned this from Mary. If not directly, then from word of mouth, which was how things were done back in the Day.
There are also non-Biblical books about Mary that were not included in the Bible.

It is thought that the author of the book of Luke was close to Mary the mother of Jesus. It appears that Matthew, Mark and Luke all used Mark as an outline and added facts. John told his own personal story all together. (No Nativity story in John.)
edit: Sorry if anyone read this before I straightened it out . I think I earned one of those perfect awards on this one.

Nobody knows. Nobody actually wrote down the books of the New Testament until after the events. Nobody knows with certainty who actually wrote them down. And other than scripture, the only things we know much about Jesus was his death. And that comes from Tacitus, a hundred years after the fact. But if one can believe in the supernatural, one is probably not epistemologically fussy.

The details of Christ’s birth were foreshadowed in the Old Testament and the Torah. In addition to Mary, as others have said, there were the shepherds who “made known abroad” what they had witnessed.

What makes you think they did?

Every culture and religion has its myths, its lore and legends, its heroic tales, etc. They report all kinds of wonderful details about which some people may express certainty but nobody really knows. How would anyone document the birth and deeds of Krishna? or Cuchulain? or Loki? How about Athena or Osiris or Pele?

From what I studied when I was intensely interested in this was that nothing was really written down as all his followers were expecting to be raised up with him. The earliest records we know of are scrolls from about 70 years after his death.

I am not the Christ. Nor was my birth videotaped or documented in any way, save for my birth certificate. Yet somehow, I know when and where I was born and some details of what led up to that night. All of this, through stories my parents told me. Recently, I told my daughter this story. Chances are, she may repeat it to her children. And someone, just might write it down someday.

My guess is it went about the same for everybody’s favorite carpenter.

I agree with @cookieman. The story of my nativity includes the Miracle of the TV. (Back in the mid fifties, my dad bough the first TV in our family the day I was born to entertain my older brother and sister.)

@Jeruba , What sets Gospels of the New Testament apart from other religious tracts is that, at least as regards the events surrounding the death of Jesus, they are given as eyewitness accounts. That being the case, it would have made sense for the writers to tell how they learned of the story of the birth of Jesus. If I had written such a work, in order to lend veracity to that part of the story, I would have indicated whether the account I gave was based on common knowledge or came from conversations with Jesus or Mary.

The first writings about The teacher and religious founder we call Jesus were written from 50 to 100 years after his apparent death.

Many of the accounts contained elements of older myths and at least two of the writers copy from the same earlier accounts which no longer exist.

Every work of fiction is also written as if it were a narrative of real events. Why would we think there’s no room for falsehood, error, imagination, or wishful thinking in some narrative of the past?

They made it up and/or plagiarised from other religions.

@Jeruba , In a novel written in first person, the narrator has to account for what is known. I am not saying the NT is fiction. That is a discussion for a different thread. I am saying that regardless of whether or not it is true, it is more credible if the writers tell how they came by their information.

You are holding the authors to today’s standards. That’s the same mistake fundamentalists make. They expect the Bible to be literally true (especially the creation and flood stories) when the mindset of the time didn’t expect that.
The first person witnesses were probably not literate enough to scribe the story and probably never even thought of it. That era didn’t demand the evidence that we do today.

The oldest known version of the New Testament is the Codex Sinaiticus, dating back some four centuries after the death of Jesus. There were older writings pertaining to Jesus dating back to the first or second century. It is not known who really wrote these, and what the motivations of these transcribers were. It is not even known if those copies were the original, or if the earliest Christians shared the same beliefs as those authors of the New Testament had. As far as I know it could have been a variety of reasons, as some have mentioned above.