Dickens uses satire in the early parts of Great Expectations to lampoon the unpleasant way Victorian guardians disciplined and guided their children. In Chapter 2, Pip explains to the reader how he was "brought up by hand" by his nasty elder sibling:
My sister, Mrs. Joe Gargery, was more than twenty years older than I, and had established a great reputation with herself and the neighbours because she had brought me up “by hand.” Having at that time to find out for myself what the expression meant, and knowing her to have a hard and heavy hand, and to be much in the habit of laying it upon her husband as well as upon me, I supposed that Joe Gargery and I were both brought up by hand.
The domineering and violent way that Mrs Joe Gargery treats both Pip and her husband is an exaggerated version of the way Victorian children were often disciplined. Corporal punishment was not only common and legal but encouraged in the upbringing of children in the 1800s. Many people put great stock in the Biblical proverb "spare the rod, spoil the child." Rather than bringing Pip up "by hand" in the usual sense of the phrase—to do so oneself, with care and attention—Dickens employs the phrase to imply that Pip and Joe Gargery both get smacked with some regularity.
This satirical commentary also incorporates verbal irony on a second level to do with Pip's psychology. As previously explained, when Mrs. Joe says she is bringing up Pip "by hand" to her friends and neighbors, she is implying that she's putting a lot of hard work into it. Pip, who in his youth takes everything quite literally, thinks she means it's literally being done "by" her "hand," as if parenting were not ever done with any of the rest of the body or the mind. Joe Gargery, a simple and biddable character, is also infantilized here, as he also apparently receives the "benefits" of this discipline. He is also part of the verbal irony of this situation, as he believes literally in the efficiency of his wife's hands-on methods.
The way Pip describes his early education in this novel mirrors many of the author's other narratives on the standard of British schooling for children. The author uses satire to poke fun at the accepted standards of learning in Pip's childhood in Chapter 7, when the narrator explains how he learned to read and write:
Mr. Wopsle’s great-aunt kept an evening school in the village; that is to say, she was a ridiculous old woman of limited means and unlimited infirmity, who used to go to sleep from six to seven every evening, in the society of youth who paid twopence per week each, for the improving opportunity of seeing her do it.
British schooling for children, especially for the poor, was in Dickens's opinion substandard at best and outright laughable at worst. To this point, the author equates the "keeping" of a schoolhouse with a supervised nap for Mrs Wopsle. When Pip tells the reader that this method "is to say" she kept a school, he is indicating the ridiculousness of paying for an education which only involves "seeing" the old woman "go to sleep from six to seven every evening."
The description of Pip's "school" quoted above is more than just the author fleshing out the nature of Pip's early (and sometimes thwarted) attempts at self-improvement. This moment of satire is a commentary by Dickens on the lax enforcement of educational standards in the country as a whole, before the regulation of public-school hours and teaching certification. The Public Education Act by the British Parliament, which attempted to resolve this problem, was ironically only passed in 1870, very soon after Dickens died.
When a character is as pompous and self-interested as Uncle Pumblechook in a Dickens novel, the author is almost always using them to satirize a "type" of character from everyday Victorian life; in this case, a privileged blowhard. When Pip is told that Pumblechook will take him to meet Miss Havisham to "make his fortune," in chapter 8, a scene of the most laughable stuffiness occurs. Pip tells the reader that he was "trussed up" in his "tightest and fearfullest suit" and
delivered over to Mr. Pumblechook, who formally received me as if he were the Sheriff, and who let off upon me the speech that I knew he had been dying to make all along: “Boy, be for ever grateful to all friends, but especially unto them which brought you up by hand!”
Pumblechook receives Pip (who is often referred to by his family as being incurably criminal) "like the Sheriff": he means to send him off to a correctional facility with a sanctimonious speech about being "for ever grateful to friends." Of course, Pumblechook is not a policeman, but merely a "peppercorny and farinaceous" old merchant, as Dickens goes on to describe him in the next chapter.
Pip, reflecting on this instance from the "future" of the novel's narration, remarks that he knew Uncle Pumblechook had been "dying all along" to preach to him about how grateful he should be for this opportunity. The reader gets the sense here and elsewhere that, in an instance of dramatic irony, Pumblechook thinks he's very important and that everyone takes him seriously. It's clear from the tone Pip strikes here, though, that that isn't his view.
The author describes Pumblechook in terms of ridiculous self-importance, lampooning men of his time who came from "new money" (not inherited wealth) with pretensions to upper-class airs, and with patronizing and undeserved moral superiority. Further, Dickens indicates that Pumblechook is materialistic, selfish, and self-absorbed in all his habits. When Pip joins him for breakfast before heading to Satis House, he says he consides Pumblechook "wretched company," as his
conversation consisted of nothing but arithmetic [...] while he sat at his ease guessing nothing, and eating bacon [...] in a gorging and gormandizing manner.
Uncle Pumblechook here and later is characterized by Pip's dramatically ironic accounts of his excess and lack of self-awareness. He preaches abstinence and thrift in others while "gorging and gormandizing," telling Pip to be grateful for the meager amount he gets while Pumblechook stuffs himself with bacon.
Although Miss Havisham herself is already quite ghoulish company, Dickens employs one of his most corrosive satires to describe her unpleasant and sycophantic family members. When Pip visits Miss Havisham in Chapter 11, he immediately dislikes her relatives, implying that they are disingenuous and false:
There were three ladies in the room and one gentleman. Before I had been standing at the window five minutes, they somehow conveyed to me that they were all toadies and humbugs, but that each of them pretended not to know that the others were toadies and humbugs: because the admission that he or she did know it, would have made him or her out to be a toady and humbug.
A "toady" is the Victorian equivalent of a yes-man, and a humbug is someone who speaks deceptively or falsely for their own benefit. The people Pip sees in the room are, sadly, Miss Havisham's only remaining family: Sarah Pocket, Camilla, Georgina, and Raymond. Havisham is certainly nasty, but she at least presents her nastiness honestly. The same cannot be said for the visitors who throng around her attempting to win her good graces. Currying favor like this is a trope in many Victorian realist novels where money is a central concern.
These people are all entirely self-serving, like many of the frivolous minor characters in Great Expectations. They are also almost totally un-self-aware, as they "pretend not to know" that they are all "toadies and humbugs" in order to preserve their delicate self-images. Havisham's family thrives on gossip and intrigue, and they are only interested in the old woman for the money they believe she will leave behind. They all protest about which of them cares for her more, protests which, the narrator indicates to the reader, are completely untrue. Each of them seems to know this about the others. They take turns jabbing at each other's attempts to be sympathetic in some very funny exchanges of cruel one-liners. At one point, Raymond makes fun of Camilla for the "nervous jerkings" she says are a result of caring too much for others:
Camilla, my dear, it is well known that your family feelings are gradually undermining you to the extent of making one of your legs shorter than the other.
The ridiculous image of hysteria shortening one leg is an example of hyperbole. Of course, this is just Dickens making fun of Camilla's hysterical excesses, as the crew work themselves up into a frenzy. This all seems quite pointless in the end, however, as Miss Havisham herself does not buy their sickly-sweet comments. She knows they are there to try and get things from her, and accuses them in the same passage of wanting to "feast on her" after she dies.