irony, where the audience knows something a character doesn't.

When Algy says that good looks "are a snare that every sensible man would like to be caught in," his remark is ironic in that a snare, by definition, takes one against one's will.

Miss Prism, upon learning that Ernest is dead, says, "What a lesson for him! I trust he will profit by it." Her remark is humorously ironic since dead men cannot profit from life's lessons.

Jack's unthinking reply to Cecily, "I haven't got a brother!" is ironic in that without realizing it he denies the lie that he has worked so hard to perpetrate, and when he tells the literal truth, Cecily won't accept it, mistaking his answer for a figurative disowning of his brother.

Cecily's long explanation of her fantasy romance with Ernest to Algernon, who is pretending to be Ernest, is highly ironic as Algy learns about things in "his" past that he has done from a woman he has only just met. Gwendolen's description of her father's role is ironic because it exchanges the expected role in society of men with that of women: "The home seems to me to be the proper sphere for the man."

The conversation between Gwendolyn and Cecily about their engagements is hilariously ironic since each of them believes the other woman is speaking of the same man when they are really only speaking of the same imaginary character who is being played by two different men.

The tea war is ironic since taking tea is usually a genteel occasion, but here it becomes aggressive, yet cloaked in exaggerated civility.

In Act 2, Wilde takes the audience on a wild ironic ride, careening from one unexpected twist to another. 

Satire is a genre of literature in which devices like irony, wit, and sarcasm are used to mock a group of people, a particular social class perhaps, an entire country, unjust laws, and so forth, with the intention of drawing attention to problems and provoking change. Satire can be harsh and acerbic (called Juvenalian), or it can be lighter and more indulgent (called Horatian). One of the major ways in which Wilde satirizes the upper classes in this Horatian satire is by pointing out their lack of morality, despite their insistence on maintaining the appearance of it. In act 2, Miss Prism says of Jack Worthing

his gravity of demeanour is especially to be commended in one so comparatively young as he is. I know no one who has a higher sense of duty and responsibility . . . . Idle merriment and triviality would be out of place in his conversation. You must remember his constant anxiety about that unfortunate young man his brother.

However, unbeknownst to Miss Prism or Cecily, Jack's young ward, Jack has invented this dissipated brother so that Jack can go to the city and pretend to be this brother, behaving badly and doing things Jack would never do in the country (an example of dramatic irony, where we know more truth than one or more of the characters). He engages in precisely the kind of idle merriment and triviality that Miss Prism believes is so antithetical to his character. Her estimation of his sense of duty helps to show how very hypocritical he is: pretending to be this morally upstanding gentleman who is really dishonest and probably somewhat disreputable (or else why would he need to invent another persona?). Wilde points out this kind of hypocrisy in both Jack and Algernon (as well as in, to a lesser extent, Gwendolen and Cecily) in order to draw attention to the bad behavior of the upper class in general.

Satire refers to the criticism of mannerisms and social behavior of specific groups using wit as a conduit of commentary. In other words, satire is a parody of something or someone (as well as a situation), but instead of it being openly criticized and talked about, the commentary is sarcastic, ironic, and subtle. Only those who are "in it" can tell the difference between something serious and something satirical.

The Importance of Being Earnest is rife with these very instances of sarcasm and irony based on the satire that Wilde creates of the very imperious English upper classes.

An instance of satire that stands out in Act 2 is the entrance of Algernon posing as bad brother Ernest in Jack's manor house, and his eventual meeting with Cecily. This is satirical in that Wilde is using two extremely shallow, clueless and seemingly careless people to represent the ideal melodramatic romance. Rather than presenting a damsel in distress being rescued by a courageous knight-like lover, we find the dyad made of Algernon and Cecily as two clueless youths without a very strong grip on reality.

For once, Cecily shows Algernon (whom she believes is Ernest) her personal diary shortly after meetiing him. What is truly satirical about this is that, in that diary, Cecily has already mapped out from beginning to end the daily goings of her imaginary relationship with Ernest even before she actually meets him. Moreover, Cecily finds it rude that Ernest (Algernon) does not remember some of the things that "took place" between them. Surely, since she invented the relationship it is impossible for Algernon to remember anything in a diary he has never read. However, this ridiculous dialogue and the asinine nature of the situation makes the entire thing so bizarre that it produces the comedy of it.

On his part, Algernon also follows along with Cecily's nonsensical rant and claims to be truly in love with her at first sight. He sees that Cecily has a weird obsession with the name Ernest, and when he asks her what she feels about the name "Algernon" he is told that

CECILY:But I don't like the name of Algernon.
ALGERNON:Well, my own dear, sweet, loving little darling, I really can't see why you should object to the name of Algernon. It is not at all a bad name. In fact, it is rather an aristocratic name. Half of the chaps who get into the Bankruptcy Court are called Algernon. But seriously, Cecily…[Moving to her]…if my name was Algy, couldn't you love me?
CECILY:[Rising.] I might respect you, Ernest, I might admire your character, but I fear that I should not be able to give you my undivided attention.

To me, the most obvious evidence of satire is that there is no one named Earnest.  There is no Earnest, he is really just the alter ego of John Worthing.  He uses the name when he is in London so that his family name is not connected with anything that he does while in town.

The importance of being Earnest is being a liar.  The idea that Gwendolyn can love someone named Earnest, when there is no one with this name who exists is ridiculous.

"Algernon's cousin, with whom Jack—as Earnest—is in love and to whom he proposes marriage. She accepts, believing him to be Algy's friend Earnest. As she explains to Jack, her "ideal has always been to love someone of the name Earnest."

The name of Earnest is bandied about by characters in this story as a shield to protect liars and lies.  It is interesting that the word earnest, according to the dictionary means:

1. "serious and intense; not joking or playful; zealous and sincere not petty or trivial; important"

"Earnest" is the exact opposite of this definition, therein lies the irony, opposite of what is expected.

It is mostly evident in the manner in which every Victorian "polite society" value and members of such highly-idolized group are mocked by being portrayed at their most exhuberant, excessive, mindless, and unintelligent.

The topic of marriage is mocked by the money-hungry ways Lady Bracknell, and the midnless dreams of Gwendolyn and Cecily.

Money is mocked through Algy's extravagance and lack of funds, hence, putting him as a person who lives way above his means.

Truth, honesty,civility and sincerity are mocked all over the play in the two-timing characters of Jack and Algy.

In all, Earnest tells us from the title to the end that this play is indeed a satire.