once used me with that insolence that in revenge I took her to pieces, sifted her, and separated her failings: I studied ’em and got ’em by rote."

Act II: Female characters, such as Mrs. Marwood and Mrs. Fainwell, are introduced. Complicating relationships are introduced, such as that between Mrs. Marwood and Fainwell. Mirabell complicates the plot action by contriving a way to entrap Lady Wishfort, who despises him for previously tricking her, so that he can contrive to win Millamant's hand in marriage with Lady Wishfort's critical blessing.

Act III: The turning point, climax, and the greatest suspense occur in Act III. Mirabell develops a scheme centering around his servant Waitwell, who will don the disguise of a fictitious Uncle Rowland to ensnare Lady Wishfort into a love affair with the promise of marriage (while Waitwell is already married to Foible) so she will have to relent and give Mrs. Millamant consent to marry and will release her fortune. Suspense is heightened when Mrs. Marwood learns all and contrives her own counter-plots.

Act IV: The falling action begins, which leads the way to the resolution. Here, secrets and twists are revealed and unraveled. Millamant consents to an audience with Mirabell. It begins propitiously when he finishes a quote by English poet John Suckling:

Millamant: Like Phœbus sung the no less am’rous boy.
Mirabell: Like Daphne she, as lovely and as coy.

Millamant and Mirabell agree, in their own ironic and playfully witty way, to be engaged and married. Mrs. Marwood reveals secrets when she sends a letter to Lady Wishfort denouncing Sir Rowland as a fraud and Mirabell as a scheming conniver.

Act V: The conflict of the play (obstacles to Mirabell and Millamant's love for each other) is resolved, and villains are ousted. The author's tone toward the subject matter is revealed and the lesson presented. Congreave's tone—hinted at through his selection of allegorical character names—toward social duplicity and manipulation for fortune and insincere advantage is revealed as being disparaging and reproachful. The lesson is embodied in the finally sincere exchange between Mirabell and Lady Wishfort in which (although still finishing off the workings of his original scheme) Mirabell offers his advice and help without expecting compensation. The villain Mrs. Marwood is expelled from the house. Millamant and Mirabell have Lady Wishfort's blessing on their marriage.

MIRABELL: Ay, madam; but that is too late, my reward is intercepted. You have disposed of her who only could have made me a compensation for all my services. But be it as it may, I am resolved I’ll serve you; you shall not be wronged in this savage manner.

Follow the link below to an article on Congreve's style in this play. In that article you will find information not only about the five-act play structure but also about the setting, dramatic elements, and so forth.

The Way of the World is part of a genre of literature called "comedy of manners," a satirical look at the "manners" of high society.

You might also read the Encyclopedia Britannica article on the play (linked below). There you will find several critical reviews.

The Way of the World was first performed in 1700, meaning that though it comes within the Restoration period, the Restoration itself was, by this time, a distant historical event which had occurred before Congreve was born. However, the play's style and content recreate the witty, licentious atmosphere of Charles II's court during the far more strait-laced reign of William III.

The most controversial Restoration characteristic of the play when it was first staged was the immorality or amorality of all the characters. Mirabell and Millamant are at the center of the play, but they are no more sympathetic or moral than anyone else. The famous outline of their future marriage given by Millamant, in which they are to be "very-strange and well-bred," is typical of the cynicism and coldness of Restoration comedy. All the principal characters are witty and detached, amusing the audience rather than attempting to gain our sympathy.

Another Restoration characteristic of the play—in which it closely resembles earlier comedies from the 1670s, such as those of Wycherley—is the complex plot, involving multiple deceptions and infidelities. Again, there is no clear difference between the machinations of the protagonists and their antagonists, such as Lady Wishfort, except that the former are more successful. The wit, cynicism, and complexity of the play are supposed to offer a realistic version, albeit a highly polished and stylized one, of the way in which the world actually works—hence the title. Over the course of the eighteenth century, popular drama was to move away from this type of writing to become much more sentimental and didactic.

The response generated is correct. The Way of the World is an example of Restoration comedy, a genre associated with the restoration of the monarchy in Britain. For your essay, you might want to discuss that Restoration comedies are generally characterized by satire including witty dialogue, bawdiness and a focus on the manners and hypocrisy of Britain's upper classes. The genre critiques "the superficiality and moral laxity of the aristocracy," as the generated response notes. 

The Way of the World contains characters typical to the genre: rakes (Mirabell), coquettes (Millamant), fops, gallants and wits who represent  various aspects of society. The story centers on the scheming and hypocrisy of Mirabell, who aims to marry Millamant for love and money and must scheme to do so. He must obtain Lady Wishfort's blessing to the marriage but she dislikes him. Her character is described in the play as "enemy to Mirabell, for having falsely pretended love to her." Thus, he must resort to lies, deceit and plots, all of which are characteristic of Restoration comedies. 

When Mr. Fainall rebukes Mirabell that,

"The discovery of your sham addresses to her [Lady Wishfort], to conceal your love to her niece, has provoked this separation.  Had you dissembled better, things might have continued in the state of nature."

In other words, it is not the deception, but the bungling of that deception that Fainall criticizes, underscoring the hypocrisy of the British upper class. Mirabel's response echoes this and also shows his moral laxity. 

I did as much as man could, with any reasonable conscience; I proceeded to the very last act of flattery with her...The devil’s in’t, if an old woman is to be flattered further, unless a man should endeavour downright personally to debauch her: and that my virtue forbade me.

Mirabell's reference to "his virtue" is ironic and satirical, which is characteristic of Restoration comedies. Even the characters' names are satirical allusions to their types. Lady Wishfort wishes to be involved with a man. Fainall urges Mirabell to be 'willing' to do almost anything to secure his desired objective.