Dumbledore binds Barty Crouch, leaves McGonagall in charge of him, and asks Snape to fetch Madam Pomfrey and Fudge. He then leads Harry to his office. There, Sirius asks what happened. Harry tunes out while Dumbledore fills Sirius in, and Fawkes comes to sit on Harry's lap. Then, Dumbledore asks Harry to tell him what happened and ignores Sirius's protests. He says that Harry needs to do this now, as it'll get harder if they postpone.
Now that Barty Crouch's true identity is known, Harry once again finds himself in the presence of adults he knows he can trust. This is why Harry is able to tell Dumbledore and Sirius what happened; he trusts them as authority figures with his best intentions in the forefront of their minds and knows they won't torment him for what he says.
Harry tells Dumbledore and Sirius everything without stopping. Dumbledore only stops Harry when Harry says that Voldemort used his blood and can now touch him. Harry loses his voice when he gets to the point where his wand connected with Voldemort's. Dumbledore explains that they experienced Priori Incantatem, the reverse spell effect, because both Harry and Voldemort's wands contain feathers from Fawkes. He says that when two twin wands are forced to fight each other, this will happen. Harry explains that he saw Cedric, Frank Bryce, Bertha Jorkins, and his parents, and tells them about Cedric's final request. Fawkes moves to the floor and lets a tear drop into Harry's wound.
Though Harry (and the reader, for that matter) would like to think that he has nothing in common with Voldemort, their twin wands and the fact that Voldemort now shares blood with Harry makes it clear that the two are connected. This reinforces that there isn't necessarily a clear line between good and evil. Instead, the differences lie in the choices people make, and everyone has the ability to choose whether to be good or bad.
Dumbledore commends Harry for his bravery and then leads Harry and Sirius, in his dog form, to the hospital wing. They enter to find Mrs. Weasley, Bill, Ron, and Hermione asking Madam Pomfrey where Harry is. Dumbledore asks Mrs. Weasley to not question Harry and to let him sleep in peace. Harry feels thankful that Dumbledore asked the others to not question him. Dumbledore promises to return after he speaks to Fudge and then leaves. As Madam Pomfrey gives Harry pajamas, he asks if the real Moody will be okay. She says he will be as Harry climbs into bed. Madam Pomfrey returns with a potion and tells Harry to drink all of it. He falls asleep after only a few mouthfuls.
By requesting that nobody question Harry, Dumbledore asks that everyone treat Harry with empathy in a situation where doing so is difficult, as everyone surely wants to know what happened. The fact that everyone honors Dumbledore's request shows that they're people Harry can trust to care for him, both as authority figures (in the case of Mrs. Weasley and Bill) and as friends (in the case of Ron and Hermione).
Harry feels warm and sleepy when he wakes up again. He hears Mrs. Weasley, Ron, Hermione, and Bill hissing that the noise will wake him and Harry hears McGonagall and Fudge's voices coming closer. McGonagall screeches that Fudge shouldn't have brought "it" inside as they burst into the wing, accompanied by Snape. Dumbledore appears and McGonagall shrieks that Fudge brought a dementor with him, and the dementor performed the Kiss on Barty Crouch. Fudge insists this isn't a loss and that Barty Crouch was out of his mind anyway, but Dumbledore says that Barty Crouch was perfectly sane and Voldemort was giving him instructions.
The revelation that Fudge acted without consulting anyone shows that, like Mr. Crouch, Fudge places more importance on his title and his station than anything else and is willing to use them to do whatever he wants, rather than using his power to do something good. His insistence that Barty Crouch was insane also shows that Fudge isn't capable of listening carefully or indeed, taking Truth Potions seriously--Snape explained earlier in the novel that they're guaranteed to work.
Dumbledore explains what he heard Barty Crouch say under the influence of Veritaserum, but Fudge insists that Voldemort can't be back. Dumbledore invites Fudge to his office and refuses to let him question Harry, but Fudge smiles strangely and asks if Dumbledore really believes Harry and a "lunatic murderer,” meaning Barty. Harry quietly says that Fudge has been reading Rita Skeeter. Though Fudge looks a bit embarrassed, he says he wasn't happy to learn that Harry is a Parselmouth and has "funny turns." Dumbledore sternly insists that Harry is sane and Harry shouts that he saw Voldemort and lists names of Death Eaters. Fudge angrily says that Harry's stories get weirder every year and he's not trustworthy. McGonagall points out that Cedric and Mr. Crouch are dead, but Fudge accuses them of destabilizing the Wizarding world.
When Harry correctly ascertains that Fudge doesn't believe him because of what Rita Skeeter wrote about him, it again shows that what Harry is fighting against isn't necessarily Voldemort. Instead, Harry is fighting to make sure that the truth is heard by all and is doing so in a society where the media aren't willing to listen to truth--it's likely in their best interests to go along with whatever Fudge says, given how he behaved in regards to Barty Crouch. Additionally, Fudge's refusal to believe Harry on the grounds that Harry is a Parselmouth exposes his prejudice.
Harry can barely believe that Fudge is refusing to listen. Dumbledore tells Fudge what he should do: remove the dementors from Azkaban, as they'll support Voldemort and let prisoners go, and then send envoys to the giants before Voldemort promises them rights and freedom. Fudge thinks both of these suggestions are crazy and that doing either will end his career. Dumbledore angrily says that if Fudge acts, he'll be remembered as being brave and great, while he'll be solely responsible for Voldemort's return if he does nothing. He continues that this is the end of their relationship if Fudge won't see reason.
Dumbledore's insistence that the giants want rights and freedom opens up the novel to explore the magical creatures that do want the exact rights and freedoms that Hermione is currently wasting her time trying to get for house-elves. This suggests that Hermione's unwillingness to listen to the house-elves is blinding her to the many creatures that would want her help, again showing that her activism is ineffective.
Fudge says once more that Voldemort can't be back and recoils when Snape shows Fudge the Dark Mark on his arm. Snape explains how the Mark works: when Voldemort touches a Mark, all Death Eaters are to Apparate to him. He says that this is why Karkaroff fled. Fudge curtly whispers that he needs to return to the Ministry and he drops Harry's winnings from the Tournament on the nightstand.
Because Snape is an insider to Voldemort's inner workings, Fudge should trust him: Snape has no reason to lie and Dumbledore trusts that Snape is on his side. Fudge's unwillingness to believe Harry indicates that in future installments, the conflict will shift to whether or not Harry is believed.
Dumbledore asks Mrs. Weasley help spread the news in the Ministry, and Bill leaves to tell Mr. Weasley. He then asks McGonagall to fetch Hagrid and Madame Maxime and sends Madam Pomfrey to care for Winky. With them gone, he asks Sirius to take his human form. Mrs. Weasley screams, while Snape looks furious. Dumbledore sternly asks Snape and Sirius to shake hands, as they're on the same side. Then, he sends Sirius to alert "the old crowd" and tells Snape that it's time to do what he knows he must. Snape leaves, an odd look in his eyes, and Dumbledore follows.
By making Snape and Sirius shake hands, Dumbledore continues in his role as a teacher to show these men that even though they're adults, they still need to learn the value of reaching out and connecting with others in the community in times of need. When Dumbledore also makes sure that Winky receives care, it shows that he values her experience and doesn't want her to suffer.
Mrs. Weasley gives Harry the rest of his potion and suggests he focus on what to do with his money. Harry says the money should've been Cedric's and admits that he told Cedric to take the cup with him. As Harry starts to cry, Mrs. Weasley hugs him. They break apart when Hermione slams her hand against the window. Harry drinks his potion and falls asleep.
Harry's admission to Mrs. Weasley reminds Harry again that though Voldemort is ultimately to blame, his actions still have consequences, some of which can't be planned for and, noble or not, might end tragically.