What is the dramatic structure of Death of A Salesman by Arthur Miller?

In Death of A Salesman by Arthur Miller, the exposition of the play lays the groundwork for the audience’s introduction to the main character, Willy, as well as to Linda and Biff. In the opening of act 1, the audience is introduced to Willy. The stage directions note,

Willy Loman, the Salesman, enters, carrying two large sample cases. The flute plays on. He hears but is not aware of it. He is past sixty years of age, dressed quietly. Even as he crosses the stage to the doorway of the house, his exhaustion is apparent.

When Linda seems worried that Willy has returned earlier than expected, he says,

WILLY [with casual irritation]: I said nothing happened. Didn’t you hear me?

LINDA: Don’t you feel well?

WILLY: I’m tired to the death. [The flute has faded away. He sits on the bed beside her, a little numb.] I couldn’t make it. I just couldn’t make it, Linda.

LINDA [very carefully, delicately]: Where were you all day? You look terrible.

From just these few lines, we are cued in to Willy’s outlook on life. He says, “I’m tired to the death,” from which we also get foreshadowing about his ultimate death in the play, as the title suggests. That “the flute has faded away” also suggests that Willy’s life has faded away. Shortly afterwards, Willy says about his employers, “I’m the New England man. I’m vital in New England.” This is also part of the exposition. The audience will soon learn how self-delusional this statement is when it becomes apparent that he is not “vital” at all to his employer.

Then Willy asks Linda about Biff, and she replies, “You shouldn’t have criticized him, Willy, especially after he just got off the train. You mustn’t lose your temper with him.” We learn immediately about the tension between Biff and Willy, which is another element of the exposition and introduces the audience to Biff’s character.

In the next portion of the dialogue, which comprises the rising action in the play, we learn why Willy is so critical of Biff. He’s “lazy,” Willy says. He has not accomplished anything in life. Willy and Linda continue to talk about the old days and about how much promise Biff had then, which further contributes to the audience's understanding and is part of the rising action.

The next scene in the boys’ bedroom between Biff and Happy is another element of the rising action. They are also discussing the past, and the audience gets the impression that all the important characters in the Loman family are stuck in the past, presumably because they never fulfilled their original aspirations. The flashback scene when Willy returns from the New England sales trip and discusses it, as well as his outlook on life, is another element, as well as the scene between Willy and “The Woman” and Biff’s surprise visit to the hotel, which shockingly reveals to him that his father is having an affair.

The climax of the play comes towards the end when Willy realizes that Biff loves him. He says,

WILLY [after a long pause, astonished, elevated]: Isn’t that— isn’t that remarkable? Biff—he likes me!

LINDA: He loves you, Willy!

HAPPY [deeply moved]: Always did, Pop.

WILLY: Oh, Biff! [Staring wildly] He cried! Cried to me. [He is choking with his love, and now cries out his promise.] That boy—that boy is going to be magnificent! [Ben appears in the light just outside the kitchen.]

BEN: Yes, outstanding, with twenty thousand behind him.

LINDA [sensing the racing of his mind, fearfully, carefully]: Now come to bed, Willy. It’s all settled now.

WILLY [finding it difficult not to rush out of the house]: Yes, we’ll sleep. Come on. Go to sleep, Hap.”

Thereafter, the falling action follows the climax and is seen in Willy’s death and the requiem. Seemingly almost in slow motion, “Biff slowly returns to his bedroom. He and Happy gravely don their jackets. Linda slowly walks out of her room. The music has developed into a dead march” and Charley and Bernard are dressed somberly with “Linda, in clothes of mourning” and the stage direction notes they “All stare down at the grave.”

The resolution comes when in the Requiem, Biff says, “He had the wrong dreams. All, all, wrong ... He never knew who he was.” Presumably, Biff will not follow his father’s lead and make the same mistake. The conflict between Biff and Willy is resolved. Willy was happy in the knowledge that Biff loved him, and Biff is more convinced of the importance of following one’s dreams.

How are Arthur Miller's ideas about dramatic form visible in Death of a Salesman?

The article that is frequently referenced when discussing Arthur Miller and his idea of dramatic form is Miller's 1949 essay for the New York Times, Tragedy and the Common Man. In this essay, Miller famously pens his thoughts on why the middle class working man (or woman, although Miller mainly talks about men) is America's tragic hero. (Arguably, this is no longer applicable, as the idea of the 'working man' has changed throughout America's history.) Of all of his plays, Death of a Salesman most accurately takes the ideas from this essay and puts them on stage.

Some of the most pertinent ideas from this essay are:

• The tragic hero works against systemic forces. Miller writes about how the tragic hero tries his hardest, despite system-level forces working against him. In the Greek time, this was often created through the use of the state or gods working against the hero. However, in Miller's plays, it is often modernity and industrialization that works against the hero. Willy Loman works to support his family, but he is ultimately upset.
• The fear of being displaced drives tragedy. Miller argues that the everyday man understands fear in American culture like the Greek heroes understood fear. Willy Loman is haunted by a fear that he often feels he cannot express publicly.
•  Tragedy arises out of imbalance. The American Dream rests on a pursuit of happiness, but Miller's characters in Death of a Salesman find it extremely difficult to balance their lives. Miller foresees the shrinking of the middle class in his plays.

What expressionistic modes and techniques does Miller use in "Death of a Salesman"?

I don't think "expressionistic modes and techniques" is the correct phrase to use in relationship to how Arthur Miller's Death of a Salesman is presented. Certainly there are special theatrical techniques used in the play. These techniques are utilized because the play sets out to express the state of the main character's psyche, his inner world.

The play takes place during the last day of Willy Loman's life, and, in that brief time, much of his adult life is bared to the audience. To show what the playwright needs to show about Willy, his past and present co-mingle and intermesh on a single stage, and the viewer needs to know what is now and what was then. In a real sense, Willy Loman is the sum of his misfortunes, his soaring hopes and his dashed dreams. That's a lot to show in a few hours, so special techniques were employed in order to expose Willy's inner life to the audience. Here is the technique used, in Miller's own words:

The entire setting is wholly or, in some places, partially transparent. The roof-line of the house is one-dimensional; under and over it we see the apartment buildings. Before the house lies an apron, curving beyond the forestage into the orchestra. This forward area serves as the back yard as well as the locale of all Willy’s imaginings and of his city scenes. Whenever the action is in the present the actors observe the imaginary wall-lines, entering the house only through its door at the left. But in the scenes of the past these boundaries are broken, and characters enter or leave a room by stepping »through« a wall onto the forestage.

In addition, transitions between past and present are accomplished using lighting and music. After a brief time experiencing the play, it becomes clear when Willy is in the present and when his mind wanders into his past.