There are many things to keep an eye out for when studying characters in any literature. Let me list a few of them for you.
First, you can look at their lives in general. What can you tell about a character by looking at his or her birth, upbringing, education, life events, relationships, and the like? This is an essential beginning. Ask these question.
Second, you should look at the character from the perception of other characters. In other words, how do his or her family and friends perceive him or her? More insightfully, you want to know how even his or her enemies and foes view him or her. All of these perspectives will give you a multifaceted understanding of a character.