A "production" in this context is a show, an event that would be held in a theater, auditorium or other venue, often on a stage for an audience. To "put on a production" is to do all of the things necessary that are involved in "staging" such an event. "To start one on sound" is a short way of saying, "to start a workshop on the subject of sound" (that is, the technical aspects of producing sound for the actors, singers, dancers and/or musicians in a show).