When Alfre Woodard was 22, she drove from Boston to Los Angeles, only stopping in her Tulsa, Okla., hometown. The four-time Emmy winner, now 67, has been acting ever since. Woodard’s career began in theater, despite her inability to sing or dance, with help from late choreographer Lester Wilson. An early play, “So Nice, They Named It Twice,” earned Woodard her first Variety mention on April 21, 1976. Woodard continued with the 1977 off-Broadway breakout role in “For Colored Girls Who Have Considered Suicide When the Rainbow Is Enuf.” Her film debut came in 1978 with “Remember My Name.” Woodard has appeared in over 90 films, her latest as the leading actor of Neon’s “Clemency,” a drama about a death row prison warden.

How did “So Nice” influence your early career?

Rosemary Tischler, the head of casting at The Public Theater, would see me at the Tcg (Theatre Communications Group) and remembered me. I told her,...