The above answer is excellent, but not every teacher is, or can be, a multi-dimensional actor just yet. So, you must at least be a director. Remember, drama is a visual, performance art, not a closet one--it is meant to be seen and heard, not just read. By directing, you also begin to differentiate instruction (appeal to multiple learners, intelligences).
If I’m teaching Macbeth, I first assign parts two deep: two Macbeths, two Lady Macbeths, and six Witches. I hand out monologues, and we audition. This gives purpose to the reading of the poetry. Once parts are assigned, we read aloud Act I as a class.
The next day, we begin moving around the classroom “stage” or go to the auditorium if it’s available. By this time, those who haven’t been assigned roles become directors by commenting on the bad acting. So I assign them to block the act. They draw the stage and sketch out the entrances, crosses, and exits of the actors. We rehearse the act again until the lines and the movements match. By this time, the students want to know how Shakespeare would have done it, and so we listen to classically trained actors reading Act I on CD and then watch a film adaptation. As needed, I drop in mini-lessons on the Globe, his Elizabethan audience, and the nature of tragedy.
Once students have a firm grasp on Act I, we follow a similar sequence for the other four acts. After having been reassigned parts, students read each act the night before rehearsals. We rehearse selected scenes using blocking directors, and then we analyze the language of a key monologue or soliloquy in class discussion or journaling. Once students have mastered a scene, we go to an adaptation. For Macbeth, I might show the Polanski murder scene on film and then listen to the BBC murder scene on CD and have students compare these two adaptations with the ones that we rehearsed and blocked.
Near the end of the unit, students memorize and deliver Macbeth’s “Tomorrow, and tomorrow” soliloquy. To culminate, we read John Updike’s short story “Tomorrow, and Tomorrow and So Forth.” Students are given a synthesis writing task of comparing the story to the play in terms of character or theme. And if we’re lucky, we will go see Macbeth staged at a local theater.
Oedipus, Hamlet, and Death of a Salesman are all classics. You have to find a way to make connections from text-to-text, text-to-student, and text-to-community. Look at the incredible resources (teaching units, lesson plans, Q/A) on this site for specific direction. There's so much good information from so many talented people, it's almost impossible not to make those connections.