In Chapter 18, Pip learns that he is the heir to a great estate and must be educated for his new role under the tutelage of his tutor, Mr. Matthew Pocket. When Pip goes to London, he is introduced to Mr. Herbert Pocket (Matthew's son), who trains Pip in manners. He, for example, instructs him not to stick a knife into his mouth, and he tells Pip, "while the fork is reserved for that use, it is not put further in than necessary." Herbert, who calls Pip "Handel" (after a Handel piece called "The Harmonious Blacksmith"), eventually becomes Pip's good friend.
Matthew Pocket, who has a kind nature, tutors several men and directs their studies. Pip spends time reading with Mr. Pocket, who attended Harrow and Cambridge. Mr. Pocket is also the author of several books on domestic economy, and his books on the management of children and servants made him an authority in this field.
Dickens is vague about the kind of education that Matthew Pocket is expected to give Pip. At the beginning of Chapter XXIV, Pip explains what little he knows about what is expected of both him and his tutor Mr. Pocket.
After two or three days, when I had established myself in my room and had gone backwards and forwards to London several times, and had ordered all I wanted of my tradesmen, Mr. Pocket and I had a long talk together. He knew more of my intended career than I knew myself, for he referred to his having been told by Mr. Jaggers that I was not designed for any profession, and that I should be well enough educated for my destiny if I could "hold my own" with the average of young men in prosperous circumstances. I acquiesced, of course, knowing nothing to the contrary.
Pip, of course, can't go to Eton or Oxford but needs some general knowledge to "hold his own" and to be a gentleman. Dickens is reflecting his own experience, because he had little formal education himself. Matthew Pocket is invented as a character in order to explain how Pip becomes a real gentleman by the time his secret benefactor Magwitch makes his appearance in Chapter XXXIX. It is significant that Pip, who had been virtually illiterate when he came to London, is reading a book in that chapter. He says:
I had a taste for reading, and read regularly so many hours a day.
After studying with Matthew Pocket, Pip knows some fiction, essays, poetry, and philosophy in English and may have even acquired some knowledge of French and even a little Latin. He has acquired "a taste for reading," which will be an asset to him for the rest of his life. He can recognize names like Homer and Socrates, Shakespeare and Milton. In fact, he is probably as well "educated" as a lot of the spoiled rich boys who went through Eton and Oxford and learned mostly rugby and rowing. The mark of an educated man is that he is adept at reading, speaking, and writing. The fact that Great Expectations is represented as Pip's autobiography demonstrates that he has become a good writer. His interview with Magwitch in Chapter XXXIX shows, among other things, that he has become very competent in expressing himself in the King's English--to the rich delight of his benefactor from New South Wales. Magwitch wanted him to become a gentleman of leisure and not to be trained for any kind of useful calling. Pip has become what the well-meaning but ignorant and illiterate Magwitch made him, and he will eventually realize to his horror that he is nothing but a spendthrift and a fop, not unlike so many other young gentlemen of his acquaintance.
Pip has acquired some taste and discrimination in intellectual and cultural matters. This is largely due to his own reading and partly due to the influence of Matthew Pocket. It is especially significant that Pip is putatively the author of Great Expectations, which begins with these words identifying himself as the author of the entire book:
My father's family name being Pirrip, and my christian name Philip, my infant tongue could make of both names nothing longer or more explicit than Pip. So I called myself Pip, and came to be called Pip.
The quote that StephanieRR provides is a good representation of what type of training Mr. Pocket is to give Pip. To put it into words that don't belong to Dickens, Mr. Pocket is just giving him general instruction on life. There aren't specifics given, so to speak. Mr. Pocket is to make Pip like all educated men, so this education is very general.
Pip is sent to Mr. Pocket to further craft his gentlemanly image, specifically regarding how to fit in with proper London society. He teaches Pip such things as proper Victorian dining etiquette and all the best places in London to attend or any places to avoid. He is trying to make Pip indistinguishable from the other young men who were born into the life to which Pip was only recently introduced. He tells Pip that Mr. Jaggers said Pip "was not designed for any profession, but that [he] should be well enough educated for [his] destiny if [he] could 'hold [his] own' with the average of young men in prosperous circumstances (194)." Vol. II, Ch. V