Suppose for a moment that some people in antiquity wrote something that was patently false. Maybe they were reporting something they thought was true. Maybe they were deliberately trying to stage a scam. Maybe they had a differing opinion from someone and sought to make that other person look bad. The reason isn't necessarily important. What is important is what's written isn't true and there's very little if anything to contradict the false statements. Maybe it's a tale of a ship that never existed. Or a hero that performed some great deed that was all an invention of the author. Or a way to part foolish people from what little money they had.
How would historical methodology detect that falsehood? I guess a more succinct way to put it would be... What tools are at the disposal of historians to weed out historical fiction from actual history?
I know I'm asking for a pretty specific answer for a very general question, but I'm eager to understand historical methodology a bit better. Humor me? :)
There's really not much to it beyond common sense and the search for corroboration.
We look at sources to see if they agree with other evidence. We tend to become more suspicious of sources who are reporting on things they didn't see, or who are elsewhere demonstrably in error. So an historian like Diodorus Siculus can be shown to be repeating rumors, things he couldn't have seen, and so on. People still read him, but for a claim of his without any supporting evidence, the most you say is "Diodorus claimed that".
We have necessary skepticism about topics where we know we have only one side of the story-- the Romans suggest to us that the Carthaginians were very unpleasant people, perhaps practicing child sacrifice. Well, is it true? We have no Carthaginian sources, and as Rome was at war with Carthage, it's not reasonable to assume that the Romans are being even handed.
So we put together archaeological evidence, what we know from other unrelated sources who discuss Baal worship (for example, Jewish traditions), and we end up with a more convincing case that "yes, human sacrifice may have been part of their religion" -- but acknowledging that our sources, whether Christian, Jewish, or Roman could all be repeating a falsehood.
One bitterly ironic case of a knowing historical falsehood that was uncritically believed by another civilization was the discovery of the Protocols of the Elders of Zion by the Japanese after the Russo-Japanese War. Not having experience with the complexities of European anti-Semitism, some Japanese mistook it for a kind of admiring tract, and sought out good relations with Jews for that reason.
Which all comes down to "the more you know, the more you know". For some historical subjects we have tremendous amounts of information-- for others we have very little. We can be far more confident in our assessment of, say, Jefferson Davis than we can of Julius Caesar.
But even with Caesar, we've got more information than just "what someone said". We've got abundant numismatic data for example-- coins survive really well, and the Romans were in the helpful habit of sticking a lot of information about who was in power and just what their titles were on their coins. So an event like the assassination of Caesar, which we might otherwise say "well, we've really only got a small number of sources, and they could all be mistaken" -- we've also got coins struck by Brutus celebrating the event (the "Eid Mar"). Still doesn't prove that it all happened as we're told, but it makes it more likely that "yes, this probably happened in March of 44 BC".
And the Romans leave us lots of other material. There are funerary inscriptions, which frequently tell us about the activities of legions; while it's not a stretch of the imagination to think that Tacitus or Livy might have gotten something wrong, when archaeological evidence agrees with their accounts, you can say "this seems more solid".
Sources
Why March ? The Hereditary Julian "Pontifices Maximi" and the Date of Julius Caesar's Assassination
Explaining the Epigraphic Habit in the Roman Empire: The Evidence of Epitaphs