Harry writes three versions of the same note asking for information to send to Hermione, Ron, and Sirius. Hedwig is hunting, so Harry paces and resents everyone for not telling him what’s going on. When Hedwig flies in, Harry gruffly tells her to not come back until his friends have written long replies. Harry figures they'll write back promptly, as nobody can ignore a dementor attack. Hedwig doesn't return, however, and Harry stays in his bedroom for three days. He alternates between restlessness, dread, and lethargy, and he wonders if he can live with Sirius if the Ministry expels him.
Harry's confusion at this point is intense. Nobody will tell him what's going on, and he's being punished for saving his own life. When everyone else ignores him, it gives him time to dwell on this, become even angrier, and feel increasingly isolated from his world and his friends. His hope of being able to live with Sirius reminds the reader that even if Petunia is maybe on the right side here, living at the Dursleys' home long-term is still untenable for Harry.
On the fourth night, Vernon enters Harry's room, dressed in his best suit, and explains that the family (minus Harry) is going out. Harry doesn't care. A bit later, he hears a crash in the kitchen and gets up to investigate. His door unlocks itself and, wand in hand, Harry starts to creep down the stairs. He sees almost a dozen people and hears Mad-Eye Moody tell him to put his wand away and come down. Harry is suspicious until he hears Remus Lupin. The other witches and wizards say that Harry looks like his father, except he has his mother's eyes. Lupin introduces Harry to the wizards and explains that they're taking him to a secret location.
When the witches and wizards take care to verbally situate Harry as looking like his parents, it allows Harry to feel connected to family that he loves and misses, as well as to the world his parents inhabited. As another mentor figure, Lupin is able to make Harry feel comfortable and trust that he's in good hands. This reminds Harry that he does have people to look to for help when he needs it, and they'll always come for him.
Harry tries to ask about Voldemort, but Moody insists they can't discuss anything here. He pops out his magical eye, which he says has been sticking since "that scum" wore it, and asks for a glass of water. Moody tosses his eye in, makes it spin, and sends a witch named Tonks to help Harry pack. As Harry throws things in his trunk, Tonks decides she doesn't like her purple hair and it changes to hot pink. She explains that she's a Metamorphmagus, which means she can change her appearance at will. It makes her a great Auror, though she's clumsy and not good at household spells. Tonks makes Harry's belongings fly into his trunk, cleans Hedwig's cage, and levitates his trunk down the stairs.
Tonks introduces Harry to a real Auror who’s young and extremely relatable: unlike Moody, who's eccentric but seems to be good at everything, Tonks admits that she struggles with some things. This helps Harry to start to understand that as he grows up, he can be a multifaceted adult in the world—the fact that he's a poor student in Potions and Divination isn't necessarily going to matter or hold him back once he's grown. Here Moody also references the previous book, in which a Death Eater impersonated him and wore his magical eye.
In the kitchen, Lupin seals an envelope to leave for the Dursleys. Moody puts a Disillusionment Charm on Harry, which makes his body like a chameleon, changing colors to match its background so that he’s almost invisible. Everyone steps outside with broomsticks and Moody gives instructions. He tells Harry that there's a rear guard in case they die, but Kingsley Shacklebolt assures Harry that nobody will die. They all take off on their brooms. Harry is thrilled to be flying, but he soon becomes cold and numb with the altitude. Finally, they dismount in a small, poorly kept square surrounded by grubby houses. Using a magical device borrowed from Dumbledore, Moody captures the lights from the streetlamps, making the street dark, and gives Harry a piece of parchment to read and memorize. It says that the headquarters of the Order of the Phoenix are at number twelve, Grimmauld Place.
Kingsley's calming nature continues to show Harry that adults in the Wizarding world are endlessly varied and in the case of Kingsley, have skills (in this case, interpersonal communication skills) that aren't necessarily magical, but still can make life easier and more pleasant. To this end, while Moody is clearly good at planning Harry's journey from Privet Drive to Grimmauld Place and planning for the worst, he's comically horrendous at making Harry feel like this is a safe operation. The device Moody uses to put out the streetlights calls back to the first scene of the very first book, when Dumbledore arrived at Privet Drive to drop off the baby Harry.