Historians and archaeologists use multiple sources to verify a claim, whether contemporary history or data recovered from sites. The Battle of Alesia is a good example of an iffy historical event with plenty of actual evidence, yet no real definitive location.

Multiple authors (Dio Cassuss, Strabo, Diodorus) placed the region known as the terrority of the Serquani, which were the people that Cesar was battling. Cesar himself wrote of the battle in Commentarii de Bella Gallico, detailing it pretty extensively and having his campaign verified as a true historical event. Through the memoir he details multiple other battles, some able to be proven and others not. So it doesn't mean the book is infallible but it does hold historical relevance. So they start with this book and try to find the location.

Alesia was an oppida (fortified settlement) that was claimed to have two hills on either side. Archaeologists from the 1800s onward found extensive evidence - in an area that matched the description- of Roman battle camps and sites. They are not too sure about the exact location and arguments range from the hill was too small, the rivers were actually streams, the area couldn't accommodate the battle force, etc. However, an oppida that fits the time period has been found with extensive roman siege works present. Coins from all reaches of the Roman Empire have also been found at these sites, indicating a coalition of troops present in this region. Local coins found were also from the Sequani terrority, including those picturing Vercingetorix (leader of the Gauls of this time). Then the leader Vercingetorix himself surrendered during this battle, ending the Gallic Wars once he was publicly garroted.

So they have multiple documentary sources, including a primary source from one of the battle commanders. The archaeological evidence aligns with these sources through artifacts such as coins, terrain features, and siege works of the Roman kind used during this exact period. Now, none of this is definitive proof and archaeologists still argue over the location -- but none of them argued that the battle occurred.

So a good answer is they work off multiple sources, develop new evidence, and approach the questions understanding their sources may be biased as they search for answers.

History is often presented as fact, but generally, it isn't. Piecing together history is a difficult, slow, and complex task. A lot of it are assumptions, inferences, and deductions, but that doesn't mean our view of history cannot be trusted.
The historical narratives told in sources should always be viewed with a healthy dose of skepticism. They are often biased and likely altered through the various translations they have undergone or having been rewritten and/or copied throughout the centuries. First thing historians do before reading a text is trying to understand who wrote it, so they can understand what likely biases are present. Is a text written by a known anti-emperor person? Then it is likely that whatever he writes about emperors should be scrutinized. Same goes for when something was written. Trends in literature, writing style, or philosophy and many other cultural phenomena can have a significant effect on written texts. All that needs to be taken into account. Subsequently, it also needs to be determined why a text was written. Was it written with a specific purpose in mind? And if so, what purpose was that? All these things give historians an idea about how trustworthy a source is, and what they should watch out for when reading and interpreting the text.
After establishing the credibility of a text based on its author, era, and purpose, it's important to try and verify the information it contains. This can happen by cross-referencing with other sources. Do three different authors all write about the same thing, and do none of them have any connections with each other? Then it's likely the event they wrote about happened close to the way they say it did. This is a difficult endeavor however, as many ancient authors drew on each other and used others' work as references. There are entire studies devoted to trying to establish which authors influences which and who they used as sources themselves. Regardless, if you can find various unrelated authors all telling similar stories, that adds a lot to the trustworthiness of the story.
Additionally a lot of matters can not only be cross-referenced with other texts, but also with the archaeological record. If an author claims a million people died during a plague event, you'd expect to find some evidence of that. An increase in graves, dedications to healing gods, protective inscriptions, signs of social unrest, etc... Wars leave big marks too. A siege would leave extensive damage on walls, economic troubles would result in a change in the economy reflected in the quantity and quality of coins. All in all there are many ways to verify the stories told in written texts by looking at the physical remains we have found.
If you take all these things together historians come up with a lot of well-supported theories about the most likely way historical events happened. If these theories are supported by enough evidence from texts and physical evidence, it becomes historical fact. Many of the big lines in history and the more famous events have all been scrutinized and our interpretations of them are supported by a ton of evidence. It is unlikely we are way off the mark and things happened entirely differently than we think it did. This certainty diminishes with more obscure events. This means that over time our view of historical fact can change, depending on what kind of new evidence or different interpretations we can find. Every day we could find something that changes our entire idea of how history took place, but since we have so much supporting evidence, it is unlikely that will ever happen on a large scale. But our idea of how smaller and badly documented events took place can change based on new information we come across.
So in short: historical facts aren't really facts, they're just incredibly well-supported theories with lots of circumstantial evidence. Historians do everything they can to verify how reliable historical texts are, and take that into account when interpreting the path of history.