I especially mean ancient secondary/indirect sources like the Ad Urbe Condita Libri (Livy) or Parallel Lives (Plutarch), but the question also applied to primary sources.
Is it simply looking to see if other works say the same thing? Is it through archaeological evidence? Is there a third method that isn't immediately obvious?
I answered a similar question not too long ago and I hope this answer will help you: https://www.reddit.com/r/AskHistorians/comments/6831u8/how_do_we_know_that_roman_texts_are_authentic/dgw272h/
As far as how do we verify if what Livy, Plutarch, Tactius, or any other author says is true, well it comes down to critically analyzing the text. Take Livy, when he tells us about the very earliest parts of Roman history such as tales of the kings or the founding of the Republic he's working of material which we have no means of verifying, but for things closer to his own time like the Punic wars, we have other sources we can compare with Livy. Sometimes Archaeology can help, for example inscriptions on buildings can help us date events in an emperors reign. Some times he have to take things of faith, when he have a source that is reliable in the areas that we can be sure about, we might be inclined to take the areas we can't verify are on a par as far as reliability.