This particular story revolves around the primary conflicts of race and religion. Ruth knows her race and her faith, but she has seen great hypocrisy and evil (primarily through her father) in the church and in the South. It does not get much better with her family in the North, but she does find some form of acceptance in the black Christian community. James struggles all of his life (until he finally gets his questions answered) with the consequences of his mother's race and religious deceptions, among other things. A character sketch will show how each of those conflicts shapes who James and Ruth become and how they react to the world. If you have finished reading, you should have plenty of material for an effective analysis of character.
You want to start by describing the characters, and what makes up thier lives. Those dimensions are important elements of the characters and what makes them who they are. If you are confused about the characters, you can also view this page:
The word "dimensions" in this context means looking at these different aspects of each protagonist. For example, Ruth was brought up in an Orthodox Jewish home, and then converted to Christianity, marrying a minister, twice, as I recall. How did this affect her life? How did this affect her family? The author, of course, was brought up as a Christian and the son of a minister. How did this affect his life? Ruth was raised in a Jewish immigrant community. How did this affect her? The author was raised in an African-American community, but he was sent to a white school. What about the experiences that Ruth endured as a child? How did these affect her psychologically? Did those psychological effects affect the author as he was growing up? Did Ruth's unusual personality affect the author? These are all dimensions of the protagonists that you can write about.