Several readers have asked about wizard literacy: where, they want to know, do wizards learn what Muggles call "Language Arts"? Other readers want to know more about Wizarding language generally.
Wizard children usually read incessantly from the time they can talk, and their parents usually teach them their letters along with other basic skills like tying their laces. (Incidentally, contrary to popular belief, many adult wizards do their shoe-laces and such things by hand: the spells required to do them by magic are simple, but they require about as much energy and concentration as tying up by hand.)
Wizarding families therefore read a great deal, and almost never have televisions. They are therefore a very bookish lot, and most wizarding children are surrounded by books from birth.
But not just any books, and not books like Muggles read: it's relatively recently that Flourish and Blots and other bookstores have made much use of "printing." Of course many Wizarding books are exactly like Muggle books, with the words fixed on the page: printing favors that format because it requires no real magical skill.
Quite often, though, a poet, novelist, spell-book writer, or essayist will magically compose his book (often, but not always, in highly magical runes) so that it "converses" with the reader, preserving something of the author's self in the text in much the same way that a portrait does. Tom Riddle's diary and the insults of the Marauder's Map were not unusual in the magic that allowed them to "talk back" to the reader, but rather in their ingenious use of the complex spells required. In the case of the diary, Riddle had also managed to conceal behind the usual spells a fragment of his soul, not merely an imprint of the totality of himself. (In another essay, I'll look at what that says about the nature of a horcrux.)
Usually, therefore, families will pass on books of ancient lore and wisdom and style that vary subtly from reading to reading and from reader to reader, but always in the style and language of the author. (One novelist, Kaiwen Llwys, was so perplexed at how to end her own story that I have read her book twenty times and the ending has been different each time.) This means that books become teachers, and young wizards read with a unique passion. Imagine what it would mean if you could read anything you like and ask questions of the text and have the text respond in the very voice of Dante or Newton or Flaubert! (The best Muggle writers tend to have a form of this magic in them and bear many re-readings, but their texts themselves remain stable.)
Of course spell-books and the like are everywhere, but over thousands of years, the Wizarding World has developed its own legends, myths, stories, and literary habits. Some of the most stern books are these myths. If a Wizarding child interrupts, say, Beadle the Bard in his tale, he is likely to be coldly ignored as the purposeful old story-teller forges ahead. There was almost no variation in my many, many readings of the Tale of the Three Brothers: the book was highly magical, but not apt to change much. Thus, in Harry Potter and the Deathly Hallows, when Rufus Scrimgeour asked me if Dumbledore and I had discussed "codes," Ms. Rowling is actually using a shorthand for a long conversation that we had about the ways in which the book could vary itself. I, having just received the book, could only reassure the Minister that Dumbledore had not taught me how to make the book say something that it would not say to the Ministry specialists.
Illiterate wizards generally have difficulty getting along in the world. More than one great wizard's family has been brought low because of a prideful belief that they had nothing to learn from books, or were too lazy to read, and a lack of familiarity with the great wizarding texts shows in one's conversation. The Gaunt family is an example of such a family: once great, wealthy, and powerful, inbreeding and inattention to learning sapped their power. I have sometimes wondered if Parseltongue did not have something to do with it: that cthonic language brings its own sort of wisdom, but it neglects much of the higher magical mind.
"Humble as a reader" and "Too proud for the page" are time-worn saws among witches that refer to the habit of neglecting one's reading.
Indeed, one of the biggest handicaps that modern Muggle-borns have at Hogwarts tends to be a lack of facility with language. In Ms. Rowling's books, perhaps the hardest thing to convey would have been the marked and obvious difference between the speaking styles of Muggle-borns and Wizard-borns. While Wizarding children might have picked up words like "Wow!" or "Cool!" or even "Wizard!", it might take a Muggle-born a few years to feel comfortable saying (as a prefect said to me my first night at Hogwarts), "Whence thy family?"
Ms. Rowling, in her books, minimizes this considerably, perhaps because she does not wish to confuse or distract readers. But it was a noticeable feature of life at Hogwarts. For instance, she describes Ernie Macmillan as "pompous," but this sometimes seemed true because he spoke a very literary 17th century style of English, not unlike Shakespeare's. His family was steeped in Renaissance alchemical literature, and though they were quite friendly they had little contact with Muggles or even more modern Wizards such as the Weasleys. When he shook Harry's hand, for instance, he was apt to use the formal "Ye" instead of "you" or even "thou" (which many Wizards still use today). A conversation with Cormac McClagen could feel like a scene from Robert Burns, and Ms. Rowling mercifully leaves undescribed some of his taste for scenes of violent passion.
Because Wizards are less apt to have any "normalizing" culture, such as television or YouTube, local communities of wizards will tend to have their own linguistic and literary style. ("High style," the common language of academics, trade, and politics, frequently sounds like a pastiche of 17th century and 19th century English, with a bit of rough Latin worked into it.)
The language which Dumbledore used to undo the charms over Hogwarts when he and Harry arrived by broomstick on the night Dumbledore died was almost certainly Anglo-Saxon: when Harry described it to me, he said it sounded "like German." Dumbledore's great-grandfather actually spoke Anglo-Saxon at home with his family: it was the cradle-tongue of several families in Godric's Hollow as late as the beginning of the 20th century. I have not been able to discover if this was true of the Potters. (It was, however, according to Sirius Black, a great joke among The Marauders that the Anglo-Saxon James Potter married the very Welsh Lily Evans.)