Harry, bleeding, pushes out of his bedroom, steps on a cup of tea—probably a trap set by Dudley—and rinses his hand in the bathroom. He sighs, wishing he could perform magic, but thinks that he doesn't know how to heal wounds anyway. Harry returns to his room and carefully looks through the bottom of his school trunk, where he finds the thing that made him bleed: a piece of an enchanted mirror that Sirius gave him. He puts it on top of the Daily Prophet, feeling bitter and sad, and finishes clearing out his trunk. He packs what he's taking with him in a rucksack.
Though Harry turns out to be wrong about the tea being a booby trap, it's worth noting that his assessment makes sense given his past relationship with Dudley. However, the very fact that Harry is wrong creates the possibility that even "bad guys" like Dudley have the capacity to change—but that their changes will really only be meaningful if Harry finds it in himself to forgive and see these acts of kindness for what they are.
Hedwig ignores Harry as he begins to go through the pile of newspapers on his desk. He finds the issue containing an obituary written by Elphias Doge about Dumbledore and sits down to read it. Doge writes about how he met Dumbledore at Hogwarts as first years, and Dumbledore was shockingly kind to him. Dumbledore arrived at school haunted by the news of his father Percival's horrific anti-Muggle crime, though Dumbledore proved to share none of his father's beliefs. He soon became famous as a brilliant student, went on to win prizes, and loved to teach. When his brother Aberforth arrived at Hogwarts three years later, the boys turned out to be very different but still great friends.
Doge's obituary reminds Harry that Dumbledore was young once too; he had to attend Hogwarts, receive an education, and come of age just like Harry is still in the process of doing. Though this is a difficult thing for Harry to process, it helps expand Harry's understanding of what it means to be an adult in the world and to see the people who are already adults as fully formed humans, not just beings who have been adults forever.
Doge writes that he and Dumbledore planned to tour the world after finishing school, but the death of Dumbledore's mother, Kendra, meant that Dumbledore couldn't come. His sister Ariana died about a year later, and Doge came home for the funeral to find Dumbledore miserable and estranged from Aberforth. Doge briefly recounts Dumbledore's biggest triumphs over the next few decades and then says that Dumbledore died working for the greater good. Harry stares at the photo of Dumbledore that accompanies the obituary and admits to himself that he didn't know Dumbledore well at all—Dumbledore never spoke about his past, and Harry never asked. Harry even thinks that what Dumbledore told him about what he saw in the Mirror of Erised was a lie. Regardless, he tucks the obituary in his knapsack.
Though Harry has, in previous novels, demonstrated great maturity by recognizing his own role in not finding things out about his friends and classmates, it's telling that, here, he blames himself for not asking Dumbledore anything as well as Dumbledore for not offering anything about his past. This suggests that, in this instance, Harry sees Dumbledore as a figure who should've performed his mentorship role differently and should've given Harry more insight into his past. Essentially, in constructing his thought in this way, Harry longs to be a child who is told things, not an adult who should've asked.
Harry turns to the most recent Prophet issue and sees an article titled "Dumbledore—The Truth at Last?" It announces Rita Skeeter's next book, a biography of Dumbledore exploring his secrets. Harry finds the rest of the article, an interview with Skeeter, and reads that she finished the 900-page book four weeks after Dumbledore's death. Skeeter laughs at Doge's insistence that the biography is devoid of facts, and promises to expose Dumbledore's youthful interest in questionable beliefs and the Dark Arts, as well as "nastiness" concerning Kendra and Ariana, and the revelation that Dumbledore's famed defeat of Grindelwald wasn't spectacular. Skeeter mentions a chapter about Harry and questions whether or not Harry's belief that Snape killed Dumbledore is a lie.
Remember that Rita Skeeter's reporting shouldn't be taken at face value; while there might be small nuggets of truth in anything that she writes, she's not known for being impartial or truthful. With this, the novel sets up one of Harry's trajectories as being one in which he learns to effectively read critically as he pieces together what actually happened to Dumbledore and what's true in Rita Skeeter's book.
Harry feels ill and angry and tosses the paper against the wall. He picks up the mirror fragment and sees a flash of a blue eye. He's sure he imagined seeing Dumbledore's eye, as Dumbledore is dead.
Though Harry knows that Dumbledore is indeed dead, his belief that he saw Dumbledore's eye speaks to the close relationship Harry had with him, and his desire for this to not end.