The idea of learning how to find one's identity is quite personal, as every person travels a different journey. James McBride in his book The Color of Water searches for his identity both in heritage and faith. His father was black and his mother is white; his father is a gentile, and his mother spends most of her life hiding (and trying to forget) that she is Jewish. That is not a typical journey of discovery.
Because identity is so personal, the best way to find meaningful and applicable quotes for yourself is to read and discover what resonates. There are a few general life-application things which might be helpful.
In chapter 14, James is spending his days loitering (and getting high) with a bunch of older black men, and one of them--known as "Chicken Man"--tells James that he has to go make something of himself because the world is not going to care enough to seek him out to discover his value. Though Chicken Man does not follow his own advice, it makes James think about what unique gifts and talents he has to offer the world; eventually he does move forward to showcase those.
In chapter 25, James shares his concluding thoughts about the journey of discovery he has been on, realizing he took the path of least resistance (in this case, claiming only his black heritage and ignoring his white). He also understands that what seemed to be a better world, in this case the white world, also had problems and issues which made life difficult. He concludes by saying he did not know who he was for so long because he chose not to look.
Finally, chapter 6 is the chapter in which the title "color of water" is explained. Ruth tells her inquisitive son that God does not pay attention to color because he is not a color--because He is spirit, He is the color of water. This is an important concept regarding identity in terms of faith and race.
As you read, you will undoubtedly find more specific quotes which are applicable to your life; however, these are good general concepts for a discussion about identity.