Actions are what make our two leading peeps so different.
Augustus is a very proactive guy. To show his affections for Hazel, he brazenly pursues her, spends time with her, and even contacts her favorite writer and arranges for her to visit him in Amsterdam. If those actions don't add up to show care and affection, we don't know what would.
Hazel, on the other hand, is so acutely aware of how her actions affect other people, that she avoids doing things for fear of hurting people. She doesn't want to date Augustus initially because she's afraid of hurting him. She doesn't cry in front of her parents because she doesn't want to be A Sadness in their lives. Bottom line: Hazel's inaction shows us as much about her as Augustus's actions do.
Hazel does a pretty good job of describing all the people in the book as they are introduced. She certainly wastes no time in describing how she sees Augustus (hint: she thinks he's hot):
I liked that he was a tenured professor in the Department of Slightly Crooked Smiles with a dual appointment in the Department of Having a Voice That Made my Skin Feel More Like Skin. (2.59)
She also does a fine job of letting us know what other characters are like based off of little traits:
My mom was really super into celebration maximization. (3.21)
Just with this one example, Hazel is able to characterize her mother as someone who tries to live life to the fullest and bring joy into it for her family. Thanks for help, H.
Hazel and Augustus are full of snarky, funny conversations, which reveal just how smart and clever they are—not to mention perfectly suited for each other. From day one they're already having funny and engaging conversations:
"We are literally in the heart of Jesus," he said. "I thought we were in a church basement, but we are literally in the heart of Jesus."
"Someone should tell Jesus," I said. "I mean it's gotta be dangerous, storing children with cancer in your heart." (1.84-95)
Through their dialogue, we can see that they have a connection that no other characters in the book have.
We get to hear a lot about everyone's opinion in this book, since Hazel and her cohorts are always talking about big topics like religion, literature, life, and death. Through their opinions, we get to see how all the characters think and interact with the world. We see that Hazel's parents just want her to be safe and happy, that Augustus's parents are very religious and conservative, that Augustus is pretty smart and philosophical, and that Peter Van Houten is one bleak, mean dude.
But most of all, we get to hear about Hazel's opinions, which are super important to the story. Hazel thinks far more than she acts, and she has a darkly humorous take on everything:
[…] and listened to Patrick recount for the thousandth time his depressingly miserable life story… waiting, as we all do, for the sword of Damocles to give him the relief that he escaped lo those many years ago when cancer took both of his nuts but spared what only the most generous soul would call his life.
AND YOU TOO MIGHT BE SO LUCKY! (1.6-7)
Her opinion on cancer and how other people characterize cancer survivors is vastly different from the trope of the beaten down, long-suffering cancer patient. She knows that there's ugliness and grief involved in the process, but she is strong and smart enough to find the humor and keep moving… both for her sake and for the sake of the people that she loves.