Claudia provides the bulk of the narration in the book. This is convenient because she actually witnessed what happened to Pecola as well as the way the town spoke about her, and she makes sure to include snatches of these conversations in her narration.
Claudia narrates her story from two different perspectives. In the Prologue and final chapter, the adult Claudia uses the past tense to describe events that happened back in 1941 in Lorain. But for the bulk of her narration, Claudia uses the present tense to describe these events, which has the effect of showing us things through her 9-year-old eyes.
Occasionally Claudia will move between the two modes, allowing us to see how she is reflecting on her own experience and highlighting the act of narration. Claudia is a highly empathetic narrator, and while she doesn't have access to the minds of the people she describes, she does her best to try to understand them, especially Pecola.
In the chapters that deal with the Breedloves and the one featuring Soaphead Church, the narrator isn't Claudia, but rather a third-person omniscient narrator. This speaker is capable of moving through extreme distances of space and time. This is the voice that tells us the long history of the Breedloves' storefront, details Cholly's early sexual humiliation, and recounts Soaphead's journey from the West Indies to America.
The third-person style is useful in a book with so many complex characters. It allows us to watch their lives unfold over time, in ways we could never do if Claudia were the sole narrator.