What are some examples of humor in George Bernard Shaw's Pygmalion?

George Bernard Shaw's Pygmalion contains many examples of humor; the play lampoons the rigid British class system of the Victorian era.

Because this play satirizes the types that the characters represent, the personage of Professor Henry Higgins is that of the intellectual who is impatient with society and prone to sarcasm. When Colonel Pickering proposes a wager that he can teach the flower girl they encounter to speak so well that she will fool the upper class at the ambassador's garden party, Higgins looks at Liza and is tempted. 

This dialogue between Higgins and Pickering in act 2 demonstrates sarcasm:

HIGGINS [tempted, looking at her] It's almost irresistible! She's so deliciously low—so horribly dirty—
LIZA [protesting extremely] . . . I ain't dirty: I washed my face and hands afore I come, I did.
PICKERING You're certainly not going to turn her head with flattery, Higgins.

Professor Higgins grows excited at the prospect of molding "a guttersnipe" into a fake "duchess." He tells Mrs. Pearce, his housekeeper, to take Liza away and "clean her." He also instructs Mrs. Pearce to burn Liza's clothes. Then he instructs Mrs. Pearce to call his servants and have them procure new clothes. In the meantime, he dismissively suggests that Mrs. Pearce simply "[Wrap] her up in brown paper" until these clothes arrive.

Further, Shaw satirizes the upper-class snobbery when Pickering asks Higgins if it has ever occurred to him that "the girl has some feelings."

HIGGINS [looking critically at her] Oh no, I don't think so. Not any feelings that we need bother about. [Cheerily] Have you, Eliza?

Ironic humor is also part of Shaw's satire, and, in act 3, there is this irony when Shaw ridicules the falseness of the upper class when Higgins has Liza come to his mother's house where she has invited some guests. The guests are impressed with the loveliness of Liza, who poses as Miss Doolittle. The conversation goes well until Mrs. Eynsford Hill brings up the subject of influenza, and Liza comments that her aunt died of influenza. However, Liza, who falls back into her own dialect, adds that she thinks those with whom her aunt lived were responsible for "doing her in" because this same aunt had survived diphtheria.

When Mrs. Hill asks what "doing her in" means, Higgins quickly "explains" that this is the "new small talk" for killing her. Liza continues to speak in her real dialect, elaborating upon her aunt's death. She explains the relationship her uncle had with her aunt, saying his conscience always bothered him while he was sober, but if he had "a drop of booze," he became happy. Unfortunately, when his wife came down with influenza, he kept "ladling gin down her [the aunt's] throat until the poor woman sat up, bit the spoon, and died." Among her listeners is Freddy Eynsford Hill, the son of the lady to whom Liza speaks. He is delighted, believing that she is conversing figuratively and colorfully.

FREDDY The new small talk. You do it so awfully well.

Professor Higgins clears his throat nervously as he rises from his chair, and Liza quickly glances at him and understands.

LISA Well I must go. So pleased to have met you. Goodbye.
FREDDY. [opening the door for her] Are you walking across the Park, Miss Doolittle? If so—
LIZA Not bloody likely. . . . I am going in a taxi.
MRS. EYNSFORD HILL (After the door closes.) Well, I really can't get used to the new ways.

An overarching example of the play's humor comes from how easily British society believes Eliza Doolittle, a lower class flower seller, is a member of the upper classes based on her new accent and clothing, giving lie to the idea that social class is inborn.

Shaw finds more specific ways, however, to poke fun at the superficiality of the middle classes. When Higgins brings Eliza to his mother's to see if she will "pass" as middle class, the middle-class Eynesford Hills are there. They had previously scoffed at Eliza as a flower girl on the streets. Now they don't recognize her, but are in awe of her beauty when she presents as a middle-class lady. When she uses the vulgar term "bloody," comedy ensues when they think they should adopt the word as the latest fashion.

Shaw also has fun with the supposed gentility of the middle classes in this scene. Higgins presents as his usual rude, boorish self, sits on the edge of the writing desk, which threatens to break it, almost breaks the divan, insults the guests and gets away with it all because no one questions his class status.

Another example of humor comes through Eliza's father, Mr. Doolittle. When he receives a stipend that puts him in the middle class, rather than being happy about it, he does nothing but complain about the stresses of middle-class life: he has to behave respectably, he suddenly acquires all sorts of relatives who are after him for money, and doctors, now that he can pay, want to treat him for all sorts of medical conditions. He can't get a moment's peace.

Throughout the play, Shaw skewers middle-class pretensions. 

What are some archetypes or analogies in George Bernard Shaw's Pygmalion?

An archetype is a pattern or type that occurs over and over again in literature. Shaw's Pygmalion derives from the Galatea story recounted in Ovid's Metamorphoses, and contains similar archetypes.

In Ovid's tale, the sculptor Pygmalion creates a beautiful statue of a woman. He falls in love with it and prays to Venus, the goddess of love, that it be turned into a woman. Venus grants his request and the statue becomes the human Galatea, who falls in love with her creator. 

In Shaw's play, the linguist Henry Higgins "sculpts" the lower class Eliza Doolittle into a lady, mostly by changing how she speaks, but also by teaching her the manners and bearing of an upper-class woman. He succeeds in passing her off to the highest echelons of society as a someone born to their class. 

Both tales use the archetype of the Creator: in Ovid, Pygmalion creates a statue that comes to life and in Shaw's play, Henry Higgins "creates" an upper-class woman out of the raw material of a flower seller. Both stories also represent the Transformation archetype, a common motif in literature. In both stories an important transformation takes place: a statue is transformed into a woman in one and in the other a lower class woman is transformed into a lady. 

Shaw used the Galatea story because it would provide a recognizable frame to audiences of his time period, but more importantly, to underscore how much Higgins thinks of Eliza not as a person but as a "thing" that he can mold at his will. She might as well be a statue to him. This can be seen throughout the play in his rude and dismissive treatment of her. Shaw also uses the Galatea analogy in order to disrupt it: Eliza's transformation into something "fully human" comes not when she becomes a lady, but when she is able to assert her own self-worth by standing up to Higgins. Rather than show the fully human, transformed Eliza falling in love with her creator, Shaw shows that when she comes into her humanity, Eliza walks away from Higgins. Shaw thus uses the archetypes he does to create a commentary about gender: a woman who becomes fully her own person is not necessarily going to fall into the arms of her creator, though in another ironic twist, Shaw shows that by becoming a lady, Eliza is left with little option (if she follows gender norms) but to find a husband--though it doesn't have to be Higgins. 

What is the effect of humor in GB Shaw's play, Pygmalion?

In at least some instances, the humor in Pygmalion is directed against the supercilious Professor Higgins and his social class that are so impressed with appearances and place so much value upon how one speaks, dresses, and acts when they are so easily deceived by Eliza as she performs correctly. Also, a couple of instances of humor illustrate that although Eliza is well-trained to appear as if from the upper class, she does not know how to think and to react as a gentlewoman, so she commits some rather humorous faux pas. So, Professor Higgins can not really “take a human being and change her into a quite different human being by creating a new speech for her.”

When, for instance, Professor Higgins visits his mother and asks permission to introduce Eliza, she makes an impression "of remarkable distinction" and when ask if it will rain, answers with pedantic correctness of pronunciation and syntax:

LIZA The shallow depression in the west of these islands is likely to move slowly in an easterly direction. There are no indications of any great change in the barometrical situation.

However, the conversation takes an ironic turn as Freddy thinks she is parodying those that consider the weather of more importance than it deserves when she replies in a similar manner a second time; he laughs, telling Liza she is "awfully funny!"

When Mrs. Eynsford Hill remarks that she does not want the weather to turn cold; she adds that there is much influenza around and spreads through families. 

LIZA My aunt died of influenza: so they said.
MRS HILL [clicks her tongue sympathetically]!!!
LIZA [in the same tragic tone] But it's my belief they done the old woman in
MRS. HIGGINS [puzzled] Done her in?
LIZA Y-e-e-e-e-s, Lord love you!...They all thought she was dead; but my father he kept ladling gin down her throat til she came to so sudden that she bit the bowl off the spoon....What call would a woman with that strength in her have to die of influenza?

In addition to the humor of Liza's ingenuous failure of falling out of her pretentious role, Shaw satirizes the upper class of the Victorian Age as Freddy delights in her language, believing it the latest "small talk" and Clara Hill leaves after repeating "Such bloody nonsense!" [Bloody means By our Lady and constitutes swearing] because Liza says it and the party believes she is using the latest form of fashionable talk.