One way to approach the complicated novel is to analyze characters and the way in which they change or do not change in narrative. The main characters of the novel are Quentin Compson, Candace Compson, Caroline Compson, Jason Compson III, Jason Compson IV, Benji Compson, Dilsey Gibson and Misses Compson. These characters undergo a lot of change as they develop, and a character assessment can show the way that their cultural values or ideas fit or do not fit into a larger framework. For example, you can analyze the way in which Quentin Compson's perspective on sexual relations coincides with cultural values in his college experience.
Another popular way to approach the novel is to analyze the way that it ruminates on cultural norms of the 1920s South. In the 1920s, the U.S. was recovering from World War I and leading up to the Great Depression. The Compson family represents an interesting case study of a family during this exciting and decadent time. An example of a good paper topic in this cultural vein could analyze the intersection of nationalism and patriotic values in Southern culture and the Compson family.
"The Sound and the Fury," as much as it critiques the personal values and cultural norms of the Compson family, also aims its focus on institutions, such as organized religion or education. For example, a paper could analyze the influence of Southern religious values on Caroline Compson's notion of family. Caroline, who seems to show favoritism toward her son Jason, seems very influenced by the social order that organized religion has instilled within her. Another paper topic could tackle the way in which Benji, a mentally handicapped boy, is marginalized by the institutions surrounding him.
A psychological approach to the novel is similar to a character study, but it focuses on what characters think, instead of what they do. The character Benji avails a particularly interesting analysis, because he is often discredited and ignored by society because of his mental handicap. A paper could analyze Benji's conception of order in terms of his own discombobulated psyche. Another paper could sift out the precursors to Quentin's suicide, analyzing the way in which his unraveling mental state mimics the unraveling of social values around him.