Read both books while highlighting important details. Pay attention to the setting and context of these stories, as well as the character development. Identify each character's motivation and the rationale for their actions.
Compare the books by looking for what they have in common. Both books are about important events that happen during World War II and feature racial or religious discrimination. Decide what is similar about the stories, such as the protagonists' ages or experiences. Look at the effect the war has had on the characters who suffer harassment, violence and aggression.
If you are writing an essay you may want to focus solely on major events or story lines. The idea is to compare these books to discover the major movements and beliefs of this period and the impact that period politics had on real people. In these books comparing both Jewish and Japanese ethnic groups humanizes their plight and shows how similar the effects of fear and racism can be, irrespective of culture.
Contrast the books by looking at the differences between the stories. In "Farewell to Manzanar," Jeanne's family is Japanese and the setting is shortly after the Japanese attack on the U.S. naval base at Pearl Harbor. In contrast, "Night" is about the Jewish experience after the Nazis reach Hungary. Contrasting involves seeing different things -- people, situations, ideas, and more -- in parallel to better understand those areas where they do not overlap.
You should already know what these stories have in common, knowledge which will make it easier for you to spot significant differences. For example, the political ideology of the Nazis, while also racially inspired, is mainly to control and "purify" the race, while in the United States, the political choice of sending the Japanese to internment camps was rooted in the fear that the Japanese were spies looking to create another Pearl Harbor.
Create a thesis statement if you are writing an essay. A thesis is a focused argument based on research that will help you make a clear point. Instead of saying you are comparing and contrasting these stories, you could develop a thesis such as, "While the justification for the internment of the Japanese in the United States and the Jews in Germany are different, both events were actually caused by racism and fear." This statement both compares and contrasts the stories while coming to a conclusion. You can then explain or justify this conclusion using examples from the books.