(Floo powder is a magic substance you thrown on fire to teleport to another destination on the Floo network.)
Harry watches Fred and George use the Weasley fireplace to go to London.
When Harry tries to do it himself, he coughs on the powder and says he wants to go to "D-Dia-gon Alley" (4.35).
Because he doesn't speak clearly, he winds up in a completely unfamiliar place: a dimly lit wizard's shop off a "dark, narrow street" (4.59).
Harry tries to get out of the shop, but he spots Draco Malfoy and his father, Lucius, coming in.
Harry hides in a cabinet and listens to their conversation.
Draco is complaining about Harry and his fame.
Lucius Malfoy wants to sell some things to the shop's owner, Mr. Borgin: "You have heard, of course, that the Ministry is conducting more raids [...] I have a few – ah – items at home that might embarrass me, if the Ministry were to call" (4.73).
Lucius and Draco get into a little tussle about Draco's grades – Lucius scolds Draco, "I would have thought you'd be ashamed that a girl of no wizard family beat you in every exam" (4.86).
When Lucius and Draco leave, Harry ducks out of his cabinet and sneaks out of the shop.
He finds himself on a street "made up entirely of shops devoted to the Dark Arts" (4.100).
This is Knockturn Alley.
Fortunately, before Harry can get into any more trouble, he hears a familiar voice shouting, "HARRY! What d'yeh think yer doin' down there?" (4.105).
It's Hagrid, the groundskeeper at Hogwarts.
Hagrid is in Knockturn Alley, buying Flesh-Eating Slug Repellent.
He guides Harry to Diagon Alley.
There, they bump into Hermione and the Weasleys almost at once.
Harry tells Mr. Weasley that he saw Lucius Malfoy in Borgin and Burkes.
Mr. Weasley is thrilled that Lucius is selling his stuff: "So he's worried [...] Oh, I'd love to get Lucius Malfoy for something" (4.135).
Mr. Weasley is also thrilled to meet Hermione's parents, who are both Muggles.
Once they have all visited Gringotts, the wizarding bank, they go their separate ways to shop.
Mrs. Weasley tells them, "We'll all meet at Flourish and Blotts in an hour to buy your schoolbooks" (4.141).
Harry, Ron, and Hermione walk off chatting happily.
At Flourish and Blotts, they see a book signing going on.
Gilderoy Lockhart, the author of their Defense books, is signing his autobiography, Magical Me.
Mrs. Weasley looks particularly thrilled to get to meet the man himself.
He is handsome and very well dressed.
There is a photographer from the newspaper the Daily Prophet snapping photos of the event.
Lockhart spots Harry in the crowd and drags him forward: "Nice big smile, Harry [...] Together, you and I are worth the front page" (4.158).
(As the Boy-Who-Lived – the baby who villain Voldemort tried to kill, only to be blasted himself – Harry is hugely famous in the wizarding world.)
After Lockhart makes a fuss over Harry, a voice hisses, "Bet you loved that, didn't you, Potter?" (4.164).
It's Draco Malfoy.
Ginny tells him, "Leave him alone, he didn't want all that!" (4.165).
Draco mocks Ginny for liking Harry, and then turns on Ron for being poor.
Meanwhile, Lucius Malfoy jeers at Mr. Weasley: "Dear me, what's the use of being a disgrace to the name of wizard if they don't even pay you well for it?" (4.176).
Mr. Weasley actually, physically attacks Lucius for his taunts.
After Hagrid pulls the two apart, Lucius hands Ginny her used Transfiguration textbook: "Here, girl – take your book – it's the best your father can give you —" (4.183).
Everyone seems a little glum as they say goodbye to Hermione and her family and head back to the Burrow.