Though Augustus may have many, many charming attributes, his driving isn't necessarily one of them.
Speed demon Augustus explains to Hazel that getting his driver's license was probably a "Cancer Perk," something that you get because people feel sorry for you.
That sounds… unsafe.
Hazel tells Augustus the whole sordid story about her disease and how everyone thought that she was going to die until she took Phalanxifor, which shrank her tumors. She also already got her GED, which impresses Augustus quite a bit.
Upon entering Augustus's home, she notices a great deal of inspiring phrases sewn onto improbable things—they're Encouragements.
She meets Augustus's parents, too. Augustus wants to watch a movie with Hazel in the dark, private basement (Ooooo!) but his parents say no way. So they grab the movie from the basement and then go back to the living room to watch.
They get to know each other a bit, the usual chitter chatter about family and interests.
It comes out that Hazel loves An Imperial Affliction and is practically evangelical about it.
Augustus gives her a book that's slightly less literary: The Price of Dawn.
Settling down, they watch V for Vendetta and Augustus doesn't even try to hold Hazel's hand.
Hazel drives herself home in Augustus's car with him riding shotgun (having been thoroughly traumatized by his driving).
When they arrive, they sit in the car and moon at each other for a little bit, until Augustus asks if he can see Hazel again tomorrow. She says she'll call him when she finishes The Price of Dawn.