How do I write a narrative story which shows a character through their thoughts? I have to present the character through the language she uses.

A narrative is a story, and can be either fiction or nonfiction. You can use characterization through the narrator and dialogue. Dialogue is conversation between characters. The narrator could include a description of the character’s thoughts. 

Since you are supposed to use the character’s thoughts, a first person narrator might be used. First-person narrators use first-person pronouns such as “I” and “we” to tell their stories. This really makes you feel close to the character.  The main character is not directly characterized by the narrator, though, because they are the same person.  The first-person narrator describing him- or herself is a little biased. For that reason, you might want to use a third-person point of view, which means the story will use third-person pronouns such as "his" or "hers."  That way, you can be inside the character’s head and describe the character’s thoughts, too.

When you talk about characterizing through language, it means we can learn a lot about a character through his or her speech patterns, dialect (local language usage), and vocabulary. We can also learn a lot about a character through how that character interprets the world around him or her. This includes how the character describes the world around him or her.