How do historians determine what really happened in the distant past and what did not?
That's a good question. In nature, history and evidence are mutually exclusive. When people ask for evidence, mostly they don't know what they are talking about. They are in a dream and they are in delusion.
There no evidence and whatsoever ever exists as long as any history is concern. History itself is a product of human witnessing instead of a product of evidence. It's only under very rare circumstance that history is considered evidenced.
To ask for evidence about history makes no difference to requesting your farther to give birth to a child in order to prove that he's actually your father. In nature male doesn't give birth to children. And in nature, history is never evidenced (under most circumstance).
Take a video tape of Ronald Legend, try to explain to the aliens that he's one of the president of the US. If you do this alone, you can never make it evidenced to the aliens, unless of course when multiple accounts of human witnessing are presented. (consider that before the creation of TV and movies, it's even more difficult for anything to be actually 'evidenced')
To put it short, people (especially those in this thread) never know what they are talking about. They think they do though.
To convey a truth of history, the following is already the best one can do:
1) write it down as you witnessed
2) willing to die for what you've written down
That's already the best can be done about a distant history.