I am NOT a biblical historian, but I have learned a little bit about it over the years so I'll give this my best shot.

Often times the dates provided in the Bible come from context clues. Speaking from a Catholic perspective, at the beginning of Christmas Midnight Mass, the cantor goes to the podium and speaks/chants a verse in providing the timeline leading to the birth of Jesus of Nazareth (Find it here.) In this, it mentions how long it has been since the rule of David, that it was the 194th Olympiad, 752 years since the foundation of Rome, 42nd year of Caesar Octavian Augustus. So those are examples of context clues used to indicate around the time of Jesus' birth.

Speaking again largely to the New Testament, books will mention certain government administrators, wars going on, events taking place in the world. Also in history we often "read against the grain" so we look for what is NOT being mentioned. If a book is still talking about Rome in the present tense, that's a pretty good indicator it's prior to 476CE.

And then of course in the modern era we can figure out when things were physically written through our dear friend archaeology. Carbon dating and techniques like this can indicate when a manuscript like the Dead Sea Scrolls or an original copy of the Gospel was created. Archaeology can be a better indicator of dates because biblical timelines and historical timelines don't always mesh, ESPECIALLY in the Old Testament. Once while in a class about Ancient Egyptian history, I asked my professor about the discrepancies between the archaeological/historical record and the biblical records. While I don't think the Bible is to be taken literally in many instances, I was interested since the books of the Pentateuch are significant texts for multiple major religions. My professor briefly looked at her watch, laughed, and said "we only have five minutes left in class, we do not have enough time to get into that."

I got some of this information from the following book. It is written by a professor, but I'd argue it has confirmation bias to it as seen just from the title alone. However, when it comes to finding and citing original manuscripts, his research is pretty good.

Brant Pitre, The Case for Jesus: The Biblical and Historical Evidence for Christ, (New York: Image, 2016)