Are they witness to the events? Did they interview witnesses? Are they reporting earlier sources? How far removed from the events are they? Say, a modern writer discussing the Roman army in Germania is referencing Tacitus' Annals, who in turn is referencing the lost German Wars by Pliny, who may or may not have had direct access to veterans of those events.
Why are they writing? To inform, or to convince? Do they have a position to support, or an enemy to denigrate?
Who are they writing for? Are they writing to the general public? Or are they writing for the current monarch about one of the monarch's ancestors?
What are their biases? How do they view the events and people they're writing about?
Are there other sources for the same events? How do they match up? Is there archaeological evidence to support the source?
When interpreting primary sources, a lot depends on when and where it was written, and what kind of source it is.
In recent times, we judge the accuracy of an account on things like whether the person telling it was an eye witness, or else interviewed multiple people to put together his or here account.
But in late antiquity and the early middle ages, eyewitnesses were generally considered unreliable (as, indeed, they are), so texts often don't make a big deal about whether or not they got their information from eyewitnesses. Instead, they throw in a number of cosmic/divine signs and portents to show that the event they're describing was known to the gods and, hence, provably true.
How do tou begin to judge the accuracy of an accou t that doesn't bother to discuss its human sources, instead backing up its version with claims that miraculous signs accompanied the events it describes? You can't read it as though it were a modern news story - if you do, you'll be bound to misunderstand it, because it's not designed to be read that way. Instead, you have to approach it much more like literature, and look at what it argues, how it makes those arguments, and what the fact that it made these particular arguments in these particular ways says about the person who wrote it, the time and place in which it was written, and - only lastly - the events it describes.
So when Livy talks about the founding of Rome, you could says that he doesn't list many sources, and talks a lot ablut unbelievable things (like Romulus and Remus being raised by wolves - for real?), and hence he shouldn't be trusted. Fair enough. But really, you get a lot more out of Livy if you ask why he is telling these stories, what kind of image of Rome he's trying to create for his audience (who is living 700 years after Rome's supposed founding), and what it says about the world in which he was living that he wrote these particular legends in these particular ways.
Often, what this means is texts written in the past tell us a lot more about their authors' worlds than the events they (claim to) describe. Texts written in the 8th century about the 5th century tell us mostly about the attitudes of the 8th century. We have to be very careful, using a lot of critical mehods and tools, before we can trust the contents. But the stories that are told always reflect the authors' interests and contexts.
This is why historians, generally, don't rely exclusively, or even primarily, on eyewitness accounts or historical documents written in the past. Instead, we study documents, court records, archaeology, literature, art - each of which also has its limits and critical issues - and then bring them into conversation with each other, and with eyewitness accounts to provide a fuller, more balanced, and more nuanced perspective on the past.
The tl;dr version of that is: all sources are unreliable. But each one is unreliable in its own way. Historians tackle this by reading between the lines - we don't trust what sources say, but instead ask why they said it, and bring different kinds of evidence together to provide a better perspective on the past than we could get by relying on the limited perspective of one source (no matter how reliable it might have been).
Do you mean primary sources, or secondary? (The distinction's blurry sometimes, but the answer will vary, depending on whether you're asking about figuring out the veracity/possible biases or blind spots of a historical document versus the reliability of, say, a contemporary scholarly article)
Some ways that I verify the reliability of the source:
There is some critical thinking involved too. When you're reading a source, does it all make sense? Are there "holes" in the logic of interpretation?