Evidence and logic.
That which does not follow by any logically valid inference from all the evidence available, is not to be believed. Everything else is to be believed in proportion to the weight of the available evidence.
This means you cannot leave evidence out; no valid conclusion can be reached from a biased sample of the evidence. And you can't rely on fallacies to reach conclusions from the evidence.
I discuss how to do this in greater detail in my books Sense and Goodness without God, Part II, and Part IV.1, and Proving History. I also recommend Bo Bennett's book Logically Fallacious and Baggini and Fosl's Philosopher's Toolkit. I give many examples of applying this method on my blog at RichardCarrier.info.