What are some quotes, with page numbers, from To Kill a Mockingbird that show Boo is quiet, shy, and misunderstood?
Since page numbers will vary from text to text, I will direct you instead to the chapters where you will find these passages.
In Chapter 8 after the fire at Miss Maudie's house, Jem and Scout realize that it was Boo who had come out of his house to put a blanket around Scout's shoulders, trying to keep her warm on one of the coldest nights in Maycomb's history. Boo's act of kindness shows how thoroughly the children had misunderstood him. Atticus, however, understands Boo's kindness and shy nature:
We better keep this and the blanket to ourselves. Someday, maybe, Scout can thank him for covering her up.
At the end of Chapter 14, Dill shows that he is beginning to understand Boo who has been misunderstood for so long. When Scout asks Dill why Boo never ran away, Dill replies, "Maybe he doesn't have anywhere to run off to . . . ." Dill is correct.
Finally, Boo's shy and gentle nature is best shown in the last chapter of the novel when he has brought Jem home after Bob Ewell's vicious attack on him and Scout. Boo stands silently in the corner of Jem's bedroom, watching Jem sleep. After Scout tells him he can touch Jem, [Boo's] hand came down lightly on Jem's hair." Boo then takes Scout's hand, and asks her in a voice that is almost a whisper, "Will you take me home?" Scout remembers that Boo's voice was "the voice of a child afraid of the dark." Scout then walks him home and never sees him again.