A literary analysis on a character can do several things:
tell the reader what a character is or is not
show how a character changes throughout a story
compare a character with another similar or dissimilar character, or
create a picture of a character for the reader. This type of analysis falls under the notion of argument because you are synthesizing information to prove an idea to the reader.
Beginning the Analysis (using Harry Potter as an example)
Make a list of all the characters ( Harry, Hermione, Ron, Luna Lovegood, Albus Dumbledore, Professor Snape…et. al)
Choose a character big enough to have a role in the story or characters that will work together in an argument and choose what you will analyze (Harry as a single character evolution or Comparison of Hermione and Luna Lovegood)
From a list of characters, question what the author has directly told you about the character(s) you are interested in – has the author directly mentioned personality traits or issues with the character?
Then question in-between the lines - S.T.E.A.L:
Speech: What does the character say and how does he or she say it? What are the meanings of what the character says?
Thought: What does this character believe about the way life is? What are these beliefs based on? How do these beliefs affect the choices this character makes? How do those beliefs change through the story?
Effect on other characters: How does this character get along with other characters in the story? Who does this character choose for friends and why does this character choose them? Where does this character stand in the social order? How does this character's social standing affect events in the story?
Actions: What choices does the character make during the course of the story? Does the character change how he or she acts? How? What affect does this change have on the character or others around the character?
Looks: What does the character look like? How does the character's physical attributes play a role in the story? How does the character change physically during the story? How does these changes affect the character's experience?
After you have looked into your character, decide what you would like to prove: character traits, character evolution, character relationships and create your thesis
Put examples into thesis/topic form
State what you are going to prove about the character(s) in the body of the paper
Be sure not to just list summary of the character or just set out to tell who the character is
EX: Over the course of the Harry Potter series by J.K. Rowling, Harry Potter evolves from a weak, dependent character to one of commanding independence. **Note: This thesis is put into a general thesis format, not X,Y, Z
EX: As evinced by his strength in speaking, his actions, and his ability to handle conflict, Harry Potter makes an evolution in character throughout the Harry Potter series by J.K. Rowling. **Note: This would be an example of an X, Y, Z thesis
EX: In J.K. Rowling’s series Harry Potter, the characters of Hermione Granger and Luna Lovegood illustrate a parallel to a powerful feminist ideal. **Note: This would be a general thesis
Put evidence within the work to illustrate your points
Find secondary sources as needed that help you prove your points