Harry wakes up the next morning and sees that it looks like Ron and Hermione fell asleep holding hands. He thinks about what will come, and feels as though Muriel's accusations about Dumbledore are poisoning his mind. He resents that Dumbledore never told him anything and wonders if Dumbledore never cared about him at all. He gets up and begins to explore the upstairs bedrooms. Someone went through them roughly. Harry wonders if it was Mundungus or Snape. He goes up another floor and enters Sirius's room. The walls are plastered in Gryffindor hangings, motorcycles, and Muggle girls in bikinis. There's one photo of Sirius, James, Lupin, and Wormtail, but it's stuck to the wall with a Permanent Sticking Charm.
It's telling that Harry's first thoughts in the morning are doubts about whether or not Dumbledore cared about him. This makes it clear that, though Harry may be afraid for his safety and worried about what comes next, he's still unreasonably fixated on information that he cannot get. Going through Sirius's room is another way that Harry is trying to get answers that aren't truly possible to obtain. While looking through Sirius's things gives Harry another look into the godfather he loved, it won't bring him any closer to reckoning with Sirius's legacy.
Looking through the detritus on the floor, Harry finds the first page of a letter that Lily wrote to Sirius, thanking him for a toy broomstick that he sent Harry for his first birthday. She writes that Bathilda came for birthday tea and that James is going stir crazy since Dumbledore has his Invisibility Cloak and he can't sneak out. The last half-sentence says that Bathilda shared something incredible about Dumbledore, but though Harry looks, he can't find the second page of the letter. He wonders why Dumbledore had the Invisibility Cloak.
Again, the letter gives Harry information that's useful and nice to have—Sirius clearly took his godfathering duties seriously and was a great gift-giver—but it raises more questions than it answers. The knowledge that Harry's parents and Bathilda Bagshot were friendly with each other, however, certainly makes Harry feel even more connected to Godric's Hollow.
Hermione shouts for Harry from downstairs, and she and Ron are angry and relieved to find him. She reads Lily's letter and then they discuss who ransacked the house. Harry suggests they go to Godric's Hollow to speak to Bathilda Bagshot, but Hermione points out that she can't help them with the Horcruxes. Harry shares what he heard at the wedding, but Hermione points out that Muriel and Rita Skeeter aren't trustworthy and tells him to not believe them. Harry thinks he still wants the truth. They start to leave for the kitchen, but on the landing, Harry stops in front of Sirius's brother's room and realizes that Regulus Arcturus Black is probably the R.A.B. from the locket. Hermione shouts for Ron.
Over the course of the series, Hermione has learned that she has to look at the context surrounding a piece of information before she can take it as fact, hence her advice to remember that Muriel and Skeeter are gossips and not trustworthy. Harry's desire for the truth, however, makes it more difficult to actually implement this advice and means that the odd things he's heard about Dumbledore begin to take on more significance, given Harry's emotional state.
The three step into the room, which is decorated with Slytherin hangings and the Black family crest. They spend an hour searching for the real locket with no success and then head downstairs. Hermione reminds Harry and Ron of all the horrible items they had to get rid of two years ago, but she stops dead when she remembers that they found a locket that none of them could open. Harry reasons that Kreacher could've stolen it, so they search his bedroom. Finally, Harry calls Kreacher and Kreacher appears in the kitchen. He forbids Kreacher from muttering insults and learns that Kreacher did steal the locket, but Mundungus Fletcher then stole "Master Regulus's locket." Harry stops Kreacher from punishing himself.
It's important to note that Harry recognizes that Kreacher is a possibly important source of information. This is something that the reader will later learn did not occur to Voldemort and, in the long run, keeps Voldemort from learning things that could be useful in achieving his goals. Harry's willingness to reach out to Kreacher shows that, at least in times like these, Harry recognizes that he has a wider community and is willing to call on others in times of need.
Crying, Kreacher says he saw Mundungus steal the locket. Harry asks Kreacher to tell them what Regulus has to do with the locket. Kreacher explains that Regulus joined the Death Eaters and, a year later, volunteered Kreacher to perform a task for Voldemort and then come home. Kreacher accompanied Voldemort to a cave by the sea and drank the potion in a basin. Voldemort left Kreacher on the island after covering the locket with more potion. The Inferi drug Kreacher under the water, but Kreacher followed orders and came home. Hermione and Ron note that elf magic is different than wizard magic, and Voldemort likely didn't consider that Kreacher would survive because of his magic.
The cave that Kreacher mentions is clearly the cave where Dumbledore took Harry at the end of the last novel, so readers familiar with Half-Blood Prince will understand how amazing it is that Kreacher made it out of the cave alive. This is Harry's first clue that Voldemort doesn't care about tapping into the different kinds of magic and information that would be available to him from sources like Kreacher or other non-human beings.
A while later, Regulus asked Kreacher to take him to the cave. There, Regulus drank the potion and told Kreacher to switch the lockets, destroy the real one, and tell nobody. Kreacher sobs that he couldn't destroy the locket. Harry asks why Kreacher was willing to betray Sirius to Voldemort when Regulus died to bring Voldemort down. Hermione points out that Kreacher is loyal to people who are kind to him, which Sirius wasn't. She notes that Narcissa and Bellatrix certainly were, which is why he passed information to them. Harry gives Kreacher a moment and then asks him to find Mundungus so they can find the locket. Kreacher nods, but dissolves into tears when Harry presents him with the fake locket.
The revelation that Regulus turned on Voldemort introduces Harry to the idea that not all of the Death Eaters are brainwashed and follow Voldemort blindly. Should Harry choose to internalize this story, this will help him see that it's possible that he has more allies on the other side than he might realize, while Kreacher's newfound loyalty to Harry suggests that Harry may have even more allies if he extends compassion and kindness to others he hasn't before.