How do historians evaluate the accuracy of their sources?

On many levels, it much easier to evaluate sources today, because we have access to so much information, whether from historical databases, archival library collections, or numerous other avenues of research. Thus, we no longer need to just assume that if so-and-so wrote it, it must have been true. What also is helpful is that historians are specially trained (many major in the subject in college or get an advanced degree); they learn research methods and are taught how to assess and evaluate the reliability of the claims and assertions the sources make.

Historians also learn that certain sources were admired in their day but might not be considered as reputable today; and they learn how to factor in the era in which the source was writing, and the state of knowledge at that time. (It is never helpful to blame someone from the 1700s for not understanding modern science, for example.) Historians are expected to recognize bias (whether political, religious, bias based on social class, etc); a good historian always has a healthy skepticism when evaluating what others have written or said. This can be very useful when reading certain sources that make exaggerated claims: a trained historian can spot something that is historically impossible, or identify areas where something could not possibly have happened that way.

Historians today also can differentiate between Propaganda and fact: when a politician claims things were so much better in the "good old days," a trained historian can examine what life was really like in a certain time period, and examine the facts about the crime rate, what the public believed about crime, how laws were enforced, etc. To sum up, historians evaluate their sources by looking at them in the context of what was happening in society when the source was writing, by comparing them to other sources in a given time, by exploring what others have said about these sources, and by fact-checking the claims these sources make.