Do you mean "How do historians address the bias that exists in the sources they use in their research?" and/or "How do historians avoid bias in their own writing?"

The answer to the former is that proper historical research acknowledges and addresses the context of the sources it uses. For example, if I am researching the Crusades and use a chronicle by a monk whose family was killed by Muslim raiders in Spain, I need to acknowledge his personal reasons for statements that may be aggressively antagonistic towards Muslims as well as any religious reasons (this is way simplified). This naturally acknowledges that one viewpoint is not entirely correct, more sources are needed to get an accurate picture of the events in question, and provides the suggestion that the audience should not necessarily take the author at their word. Using the 5Ws (Who? What? When? Where? Why?) when looking at any source material - primary, secondary, or otherwise - is a good place to start in order to understand more fully the meanings and implications of any given source.

For the second, all writers are products of their own experiences. However, by applying the theories and methods that go with the preceding paragraph, and submitting their research through academic, non-politically affiliated, and peer-reviewed channels, historians can provide scholarship that is accurate and convincing to the best of their abilities.

Keep in mind that the theories, methods, and defining characteristics of the historical field change over time, too, so the requirements needed by historians in the 19th century are different than those required by historians today. The Venerable Bede was esteemed as a historian throughout the middle ages, but his Ecclesiastical History would not have made it through to publication at Oxford University Press today as a definitive history of early medieval England.

To draw a successful and unbiased conclusion, a variety of sources must be consulted from the period in question. Individually, a source's content must be examined while also mindful of the author's own personal opinions and experiences, the overarching views of the people they are loyal to and the audience it is aimed at. After doing this with multiple independent sources, these need to be compared with one another. What's the same? What's been left out? Why has one person emphasised something more than another?

Take as an example the recollections of the final defence and fall of Constantinople to the Ottoman Turks in 1453. The city was defended by Catholic and Orthodox Greeks, Venetian merchants, local Genoese from their colony in Galata, Genoese soldiers that had come on their own expense from Italy, and other individuals. The issue was that these groups did not really get on, especially the Venetians and Genoese, and neither with the Orthodox Greeks, so recollections of the siege provide a good example of some heavily biased Greek-bashing, Venetian-bashing, Genoese-bashing, and surprisingly little Turk-bashing.

There are three main sources from the siege:

• Nicolo Barbaro - Venetian galley surgeon, present at siege but remained at one section of the wall the entire time then escaped, thinks that the Greeks are greedy and cowardly, claims that the Venetians are given the responsibility of defending the entire wall, thinks the Genoese of Galata are actively helping the Turks, says very little about the Genoese soldiers then blames them for routing at a crucial time, mentions a Turk pretender, Orhan, defending and a German (maybe Scottish) engineer called John Grant, when the Turks enter the city they systematically pillage it.

• Leonard of Chios - Genoese bishop, present at siege then escaped, also does not think much of the Greeks - unless they're Catholic, mentions Venetian defence of about a third of the stretch of the land wall, 'remains silent' on the role of the Genoese of Galata in assisting the Turks, puts the Genoese soldiers at the heart of the defence with their commander leading the entire operation, but also criticises them for routing when he is injured, mentions a Catalan consul defending, as well as John Grant. Says that the Turk entry was brutal and chaotic.

• Doukas - Catholic Greek notary, came to Constantinople soon after it fell and talked to survivors of the siege from both sides, mentions some Greek absences from the defence, the Venetians and Genoese defend roughly half the walls each and the Greeks fought alongside them both, all led by the Genoese commander, whose injury led to the weakening of the fighters but not their complete rout. Says that the Genoese of Galata actively supplied the Turks during the siege but also fought against them on the walls, mentions a Hungarian ambassador being present, talks of the final sack as rapid but ordered.

All three sources have their biases yet contain a massive wealth of information. Moreover, multiple other shorter accounts add to this by giving their side of the story. It is the job of the historian to sift, dissect and evaluate primary sources, ultimately coming out with a sound conclusion from this evidence.

Edit: Formatting.

They don't because it is nearly impossible. They try to think around it, taking into account their own personal interpretations. To take one example, the only real source that we have for the Persian wars are Greek and all the historians lived many years after the events which they describe. As such historians have to take the accounts that we have with a giant pinch of salt. We search for other records, archaeological etc, where possible but we can never get over the fact that we have only one side of the story and the rest is lost to history.

To take a more recent example, of the Dreyfus affair in which the innocent Dreyfus was sentenced falsely for espionage because of his Jewish heritage, the affair then divided France for years afterwards. the historiography is fraught with controversy with some defending Dreyfus and those that campaigned on his behalf and others who fought against his pardoning, reveling historian's own personal agendas. I think it would be best if I allowed people to go an find this and judge for themselves and not name names because I do not want my own personal view to colour that of people on this sub. Controversy and conflicting views over an affair of such huge importance should be welcomed rather than discouraged in my opinion. One example that springs to mind is Ruth Harris' wonderful book The Man on Devil's Island, when it was published there were some stringent protests from French academics that she did not treat this or that character accurately, perhaps revealing their own agenda or interpretation of the source material.

In my opinion it comes with the territory that historians and their sources have biases and agendas of their own, as do we all. They should not be avoided, but rather be exploited in order to gain an understanding of the differing perspectives involved in making and reading history.