How do historians overcome problems that they face in identifying true evidence from so much other evidence? How are they able to decide if a source is reliable or not?
It is not easy, and often not completely possible, for historians to determine which evidence is true and which is not. This is one reason why historians can disagree with one another.
When historians look at evidence from the past, the best that they can do is try to determine how credible that evidence is. Much of the evidence that historians look at is in the form of written documents. A major technique for determining whether written documents are credible is asking whether the author would have had a motive for falsifying or slanting the document. For example, imagine that you are reading the memoir of a German person who lived through World War II. That memoir says that the author and everyone they knew had no idea that Jews were being killed by the Nazi regime. This may be true, but the author has an incentive to say this because they would want to make themselves look less morally culpable for the Holocaust. By contrast, we might be more willing to believe a memoir that candidly admits having known that evil things were happening, but says that the author did not care enough about the Jews to do anything about it.
Another way to evaluate the credibility of a piece of evidence is to look at how well it fits in with other evidence that we have. For example, if we come across a piece of evidence that seems to prove that Richard Nixon knew nothing about the Watergate coverup, we would have to evaluate that in light of the fact that we have many kinds of evidence that show that he did know about it.
Neither of these techniques is infallible. History is inherently difficult to do because historians are often faced with conflicting evidence and it is not always possible to know which “side” of the evidence is accurate.