When multiple primary sources agree on something.

So, for example, you drop a book. Your brother goes away and records in his diary that you dropped the book. You tell your friend what you did and she sends a letter to someone else about your book-dropping activities. Another friend pens a satirical poem about the book you dropped. Perhaps you yourself write something much later in your life about dropping a book that one time. Years and years and years later we take all these sources and it becomes pretty abundantly clear that, although the exact date might be debated, we know that you definitely dropped a book. We can't understand your reasons, of perhaps not even why it was so important at the time, but we can say with good authority that it happened.

We can't trust any individual records from any point in history. And the problem is that the further back you go, the fewer records exist. So for really ancient history it's usually not so much a case of saying "Alexander the Great definitely slept with a copy of the Iliad beneath his pillow" as saying that Plutarch makes this claim. The more literacy increased within a culture (as well as the more records that were preserved) the easier it is to find multiple sources on an event.