The style of Richard Sheridan’s play The School for Scandal relies heavily on juxtaposition and not-so-subtle mockery. The sneering style connects to the play’s genre, which, as the question notes, falls under a comedy of manners.
As the name implies, and as other Educators have pointed out, a comedy of manners makes fun of the upper class. It shines the comedic spotlight on the socioeconomic group that is regularly imputed to possess the majority of society’s sophistication, eloquence, and manners.
The scornful, tongue-in-cheek style of Sheridan’s play is visible right away. The first scene has the noble Lady Sneerwell engaging in some not very noble activity—mainly, spreading gossip about a smattering of other noble women, including a Lady Brittle. The explicitness with which Sneerwell deviates from the expectations of her supposed cultured class could be funny to many people.
The ironic style of Sheridan’s comedy of manners is reinforced by the names that he assigns his characters. Though these are people from the upper crust of society, they don’t possess admirable names. Lady Sneerwell’s name does not reflect kindly on her; neither do the names Charles Surface, Sir Benjamin Backbite, or Miss Verjuice.
As with the first scene, the names of the characters can’t be separated from the over-the-top ridicule and blatant incongruity that’s critical to the style of Sheridan’s comedy of manners.
Sheridan's School for Scandal shows two main attributes of the Comedy of Manners style: it is satiric and it portrays characters primarily as types rather than fully rounded individuals.
School for Scandal satirizes the gossip-mongering, character assassination, hypocrisy, and greed of eighteenth-century British high society by exaggerating these flaws to create dark humor with a moral message. Sheridan clearly hopes that by holding a mirror to upper-class vices, he might make them so apparent that the rich might reform their behavior.
A large part of the satiric exaggeration in the play comes from giving a character a name that describes his or her flaw, then heightening that particular flaw. This is a technique borrowed from Medieval morality plays, in which characters were often named for either their main vice or their main virtue. Thus we have a lying and spiteful gossip appropriately named Mrs. Sneerwell: she makes a career of sneering and slandering. Her culpable dupe, who will faithfully repeat any slander without questioning its truth, is a woman called Mrs. Candour. Likewise, Mr. Snake, as his name implies, has a poisonous personality, while Benjamin Backbite enjoys mocking people behind their backs.
It's difficult to miss what these characters represent, which allows audiences to sit back and enjoy the drama that unfolds. School for Scandal was a particularly popular example of a Comedy of Manners and influenced such writers as Jane Austen, who imitated its scathing satire, and Louisa May Alcott, who picked up on its allegory. These later writers, however, rounded out Sheridan's flat characters.
Sheridan's School for Scandal is an 18th-century example of a Comedy of Manners, in which the artifice and superficiality of the upper classes are revealed. Its characters are, for the most part, types rather than deeply drawn characters, and their follies are revealed. Most of the characters change little from the start of the play until the end, and the purpose of the play is to satirize the manners and affectations of the upper class. Sheridan's play also has some elements of sentiment, unlike a traditional Comedy of Manners, in the reformation of Lady Teazle.
Lady Teazle is, at the play's start, the typical country girl who, once married to a wealthy husband, becomes spoiled and petulant. She tells her husband, Sir Peter:
I ought to have my own way in everything, and what’s more, I will too. What though I was educated in the country, I know very well that women of fashion in London are accountable to nobody after they are married (Act II, Scene 1).
Lady Teazle is a superficial and flirtatious young wife and resembles the traditional type of a young woman of fashion. In the end, however, she reforms herself and has a reconciliation with her husband, playing against type.
Lady Sneerwell is also a type--a vindictive gossip. She says at the beginning of the play:
Wounded myself, in the early part of my life, by the envenomed tongue of slander, I confess I have since known no pleasure equal to the reducing others to the level of my own injured reputation (Act I, Scene I).
Along with her partner in crime, Mr. Snake, Lady Sneerwell devotes herself to gossip-mongering to break up Charles, who she wants for herself, and Maria. In the end, even after her plot is revealed, she hasn't changed at all and remains unrepentant. She began as a woman who likes to stir up trouble and ends as one, and she is a traditional Comedy of Manners type.
"School for Scandal" is an excellent example of a Comedy of Manners. It is a blatant attack on the superficiality of the upper class, pointing up their lack of morals and misplaced attentions. In a Comedy of Manners, the characters are very clear and you know exactly who they are the moment they appear, not just by their appearance and actions, but by their names. Lady Sneerwell, Sir Benjamin Backbite, and Snake all carry their negative qualities in their names. The Surface brothers are all about what's on the surface -- Joseph appears moral but really isn't while Charles presents the opposite.
Sheridan's satire goes one step further than the Comedy of Manners that preceded it during the Restoration. In the 18th century, such foolishness required a consequence. During the Restoration, the evil doers were often not punished if they were clever and witty enough. In the 18h century, the evil-doers are punished. So, in "School for Scandal," we see the "school" members ostracized, with the exception of Lady Teazle who is truly contrite and given a second chance to live an upright life. It is for this reason that Sheridan's play is often labeled a Sentimental Comedy, to distinguish it from the Restoration Comedy of Manners.