This is a very well-researched and studied and debated area of history. Before I start, I am going to preface this that two excellent books to start out exploring are The Historical Jesus: The Life of a Mediterranean Jewish Peasant by John Dominic Crossan and Jesus: The Apocalyptic Prophet by Bart D Ehrman. Much of what I am about to say comes from these books.

First, we need to be clear on a few things. It is generally believed that a historical Jesus existed sometime in the early 1st century CE, likely dying between 25 and 35 CE. What we know beyond reasonable doubt, was that this figure did not have many followers at his time (Crossan estimates may between 30-100 at max) but it soon grew. We are reasonably certain that oral traditions of the historical Jesus started nearly immediately and that several written accounts likely began to be transcribed around the year 70 CE. It’s largely believed that Mark was the first gospel written since Matthew and Luke (written around 80 CE) both have parts of Mark in their books (verbatim) however it’s clear that Matthew and Luke weren’t getting information from each other because they both have some contradictory information from one another. It’s also largely believed there was another “gospel” produced before Matthew and Luke that is lost. This document is refereed to as Q that has since been lost to the ages. The gospel of John was possibly produced around the year 90 CE, but possibly as late at 110 CE. It is also worth noting that Paul, who never met Jesus (although claimed to have seen him in a vision of sorts) began preaching himself and he wrote his own accounts. However, he actually rarely discusses the life of the historical Jesus. If you were to write down every reference Paul makes to the historical Jesus, it would fit on an index card, that’s how infrequent it is. Still, it’s worth noting he did write about him a little and his accounts probably began to be written around 50 CE.

Today, there is an entire discipline of religious scholarship called textual criticism that focuses on examine these accounts and cross examining them to understand the truth behind these texts. The challenge is even greater than just the fact that these stories were written down decades after Jesus died - it’s that we have no original copies of any of these texts anywhere. Archives and museums around the world have collected every scrap of New Testament writing written in the original Ancient Greek and none of it dates back to the first century CE and over 94% of the over 5,700 partial and complete manuscripts were written AFTER the year 800. This leaves us with very limited information that dates back closest to the time of the source. This is important because historians from all disciplines of history value what is oldest because it’s usually what is more accurate.

I mention all of this to explain, that being able to figure out the truth behind the message of Jesus of Nazareth is one thing Historians have been trying to do for the last 300 years. Around the year 1700, an English theologian, John Mill who had access to about 100 ancient New Testament manuscripts began studying them and comparing the texts together. He found that between these ancient manuscripts, there were hundreds of thousands of errors or contradictions between them. So we’ve known for a long time that the very nature of the primary sources uses to piece together the story of Jesus is very complicated and uncertain.

The other problem is that the Bible’s people use today, such as the New International Version paste together a combination of all ancient sources together, sort if like forcing pieces of unrelated puzzles together. An example can be found by looking at some well-known stories of Jesus as depicted in the gospel and trading back earliest recordings of these stories. One of the most famous stories of Jesus is the story of him having the woman caught in the act if adultery brought to him. (John 7:53). This is a moving story where Jesus tells a group of instigators that if they wish to stone the woman to death, the person who has never sinned should cast the first stone. One by one, each accused leaves as they acknowledge that all people are sinners. However, if you trace back the story in the texts, it doesn’t appear anywhere in the original manuscripts we have of John. Our two oldest complete bibles, the Codex Sinaticus and Codex Vaticanus (both date back to the 4th century CE have no mention of this story. Actually, no ancient versions do. We don’t see this story until HUNDREDS of years later. Why is it there? Today’s bibles were assembled from Middle Ages traditions that didn’t understand anything about the ages of the texts so many non-original accounts that are missing from our earliest and best manuscripts are in people’s English bibles today.

Okay, so now let’s actually answer your question. The goal of historians is to compare many of the ancient accounts together, in their original Greek. By using critical methods of examination, they can reasonably assert which sayings of Jesus were likely his, which maybe were his, and which were unlikely his. Again, I strongly recommend checking out the books above because they can explain this in detail and provide ample pieces of evidence to help us understand who the historical Jesus was, what his beliefs were, and what he probably said. One example of this, is that historians largely agree that Jesus preached an Apocalyptic message and had his followers believing the end of the world, brought about by the Jewish God was nearing. When I was studying the history of the New Testament during my undergrad program, I was blown away by the sheer number of historians who agree on this point - and many have believed this for decades and decades. If there's one thing that many historians of this figure agree on is this: Jesus was a Jewish Rabbi who lived around Galilee in the early first century and preached that God would bring about the imminent end of the world.

Hope my answer is helpful. This isn’t my primary area of expertise, but I studied this a great deal during my undergrad, so I love discussing it. Please let me know if you have follow ups or if I was unclear on anything.

Edit, added a detail about Paul