The same way anyone else does: by comparing them to the other things we know.

This becomes more tricky the earlier back we go or the more specific a piece of information is. You can see this most acutely in Biblical studies, where people try to pin any number of textual references to actual events with little actual proof of correlation.

Historians of antiquity have relied on archaeology for a long time, and this is now something that's filtering up to the early Medieval field. Of course, we can also rely on other written sources!