When looking for how an author presents a character, like Juliet, what you are really looking for his how the author characterizes that character. Characterization refers to how the author presents the character as a person. You are looking for the traits of the character. There are a lot of different things you can look for to help you analyze for characterization, but specifically, you want to pick out what the character does, says, and even how other characters relate to that character, because all of these things can help you see what the character is like as a person. Below is a link to an article for more details on character analysis, but some things to look out for are if the character makes ethical decision, if she acts wisely or unwisely, what her motivations are, words the character frequently speaks, symbols frequently associated with the character, etc. (eNotes, "How to Write a Character Analysis").
If we are analyzing Juliet's characterization, one thing we can notice about her is that she is very self-willed. While she is respectful to her parents, it's very evident that she cares very much about her own thoughts and wishes. For example, when asked what she thinks of marriage, Juliet very directly states, "It is an honour that I dream not of," meaning, she has no desire to get married (I.iii.70). Since she so very directly expresses her own opinion here, we see that she is self-willed. However, she is also very respectful to her mother in agreeing to pay attention to Paris and decide if she can "like of Paris' love" (100).
Another thing we can see about Juliet's characterization is that she can be very rash. We especially see her rashness in her resolve to commit suicide should Friar Laurence fail to help her escape having to marry Paris. Friar Laurence's plan was to fake her death so that she can be secretly united with Romeo in Mantua. But Juliet had just been threatened to be disowned by her father should she refuse to marry Paris, so if she simply left home to be with Romeo, she would have nothing more to lose. Therefore, why go against all of the religious beliefs that earlier seemed to be so important to her by threatening to commit suicide should Friar Laurence fail to help her? Why not just ask Friar Laurence to help her get to Mantua without faking her death? Her decision of suicide shows us just how rash and impetuous her character is.