Clarisse seems to target Montag in Bradbury's Fahrenheit 451. He senses her before he actually sees or meets her, several times.
When she does finally "wait" for him, they meet, and over several meetings he is struck by how unusual she is. She pays attention to her surroundings and to nature, and her family actually talks to one another. She asks him if he's happy. She is young and lively and offbeat and looks him straight in the eyes. When he fails the dandelion test, in addition to thinking about books (as we know he's been doing for quite a while), and nature, etc., he starts thinking about his relationship to Millie.
Of course, Clarisse is not the only influence that moves Montag to self-awareness. His participation in the death of the woman who refuses to leave her books, and Millie's stomach pumping influence him as well.
Montag becomes even more dissatisfied with his life, and this leads him to attempt to change it.
To me, the way to find how Clarisse affects Montag (what she does to affect him) is to look at some of the things she asks him and some of the things she has him do. These things tend to make him have to think.
Perhaps the most obvious example of this is when Clarisse does the dandelion test on herself and then has Montag do it too. When the test "reveals" that he is not in love, this leads him to think about the nature of his relationship with Millie. Thinking about this leads him towards understanding himself and his life better.