He was an American theater director responsible for more than 100 theater productions. In 1984, he was awarded a special Drama Desk Award for service to a wide range of playwrights. He directed the American premiere of Waiting for Godot, Who's Afraid of Virginia Woolf? and Sićušna Alisa.

Schneider also directed Samuel Beckett's only direct foray into the world of film, titled Film. The short film starred Buster Keaton, and its direction is often wrongly attributed to Samuel Beckett himself, especially during the exhibition at the Louvre in November 2006. The film is a quiet exploration of Bishop Berkeley's principle 'esse est percipi' (to be is to be perceived).

He taught at the Catholic University, the City College of the City University of New York, the Juilliard School (where he was the director of the theater program), the University of California. He was also co-artistic director of The Acting Company. He was also chairman of the board of directors of the Theater Communications Group (TCG).