The answer is that it depends on the subject at hand and the available evidence. All one can do is gather all possible evidence and then make educated guesses and suppositions. There are definitely times when they have to make GIGANTIC leaps of reasoning, and there are quite a few subjects about which a consensus has been reached so everyone talks about that consensus as if it's a hard fact when it's not even close to definitively known. You have to just pick a theory and go with it sometimes in order to facilitate the teaching of others and further studying of events. The amount of available evidence determines how much is needed to start talking about it definitively. If there is only one source that talks about an event, then what they say happened will be referred to as if it did happen (a lot of the time, at least) but with a caveat once you get into studying it more deeply that things may have happened differently (especially if the source claims something that seems dubious like a three million man army in antiquity or is even impossible like a miraculous act of god - the more dubious then the less you need to study something to reach the part where historians put their disclaimer about the veracity of the event).

There are relatively few human events and/or cultures about which historians can definitively say anything. Only since the invention of the video camera have certain historical facts become absolutely undeniable. The vast majority of humanity's past begins outside the strict purview of historians, since there is no historical record at first. We really need to rely on the work of anthropologists to discover evidence about the parts of humanity's past that are outside of the historical record. Once they study and write about their findings, those writings can then enter the historical record and be used by historians. Historians can often moonlight as anthropologists (with or without calling themselves such) and discover new evidence themselves to lend credence to a pet theory of theirs.

Before the advent of anthropology as a separate field of study this would be handled by historians specializing in archaeology or prehistory, and it still is today, working alongside anthropologists in parallel (although to be honest I have no idea why someone would call themselves a historian and then say they specialize in prehistory, since that's the period that existed before the period their field studies. Why not just call yourself an anthropologist? I guess they just started studying history and decided they really liked the anthropologist's job the most but it was too late to switch majors. Archaeology is a sub field of anthropology as well but there are still a lot of archaeologists that call themselves historians instead of anthropologists for some reason).