August Wilson, the Pulitzer Prize winner who wrote the screenplays for “Fences,” “The Piano Lesson,” and “Come and Gone,” is one of America’s leading playwrights, a chronicler of the African-American experience with more than 10 plays, each set at a different time from the s. XX. Now, every year, thousands of young students gather in New York City to perform one of his monologues in a Broadway competition. Giving Voice closely follows the lives of six of those students as they develop their performances in hopes of faithfully representing Wilson’s legacy.