In writing an annotated bibliography, the instructor wants the class to compare and contrast scholars and their different approaches to the research. How is that expressed in an annotated bibliography? What are the components to the author's background?

I think what your instructor wants you to examine for this assignment is what is called historiography, which is the study of how historians interpret history.  It's not enough to look at the facts--sometimes, it is necessary to see the lens through which the historian sees the time period.  For example, for a work about the Cold War, there are many schools of thought.  One school of thought states that the Soviet Union was directly responsible for the Cold War.  Stalin's aggression after WWII alarmed the United States, and this is why the United States increased military spending and sent troops all over the world in order to defend against communism.  This was the school of thought that was prevalent during the early days of the Cold War in America.  However, by the 1960s and 70s, attitudes towards the Soviet Union began to soften in some academic circles and some historians of the period state that it was actually the Americans who were to blame.  America excluded the Soviet Union from having a say in the postwar development of Japan, and it also did not share atomic secrets with the Russians, thus creating a level of distrust with its former ally.  The Soviet bloc was Stalin's buffer zone in order to save himself from a Western attack after the fall of Germany in May 1945.  The school of thought most prevalent today is that the Cold War was the fault of both nations.  Some of these alliances between former European colonies and superpowers led to the Korean and Vietnam Wars.  
There are other examples of historiography, but this one is the easiest to explain.  In order to find out a historian's field of study, look at other books and articles he/she has written.  Historians can also be grouped by their fields of interest--some may be social historians while others may study politics or war.