Ron is beside himself about Viktor Krum as the Hogwarts students file inside. The Beauxbatons students sit at the Ravenclaw table, while the Durmstrang students sit with the Slytherins. Harry notices Filch adding four extra chairs to the head table and wonders who else is coming. The teachers file in and after they take their seats, Dumbledore addresses the students. He welcomes the guests and the feast begins. There are a number of foreign dishes on the table, which Ron refuses to touch. A girl from Beauxbatons approaches Ron and asks if she can take the bouillabaisse. Ron mouths wordlessly at her and lets her take it. He insists the girl is a veela, which makes both Harry and Hermione laugh.
Ron's reaction to the Beauxbatons girl again reminds the reader that he's beginning to mature sexually and have romantic thoughts about people, heralding another aspect of his coming of age. His inability to speak to her effectively, however, points to how young and immature Ron still is. The fact that Hermione and Harry can laugh at Ron implies that they may be slightly more mature in this regard, or at least aware of how immature Ron looks.
Hermione points out that the extra two seats have been filled by Mr. Crouch and Bagman, and says that they likely organized the event. After the feast ends, Dumbledore introduces them, as they'll be the two other judges for the Tournament. He then asks Filch to bring in "the casket." Filch carries in a huge, jewel-encrusted chest. Dumbledore explains that one champion from each school will be chosen by the Goblet of Fire, and he pulls a large cup filled with blue flames out of the casket. He says that interested students can put in their names and to keep underage students from trying, he'll draw an Age Line around the goblet. In closing, he reminds the student that putting one's name in creates a binding contract and a person can't back out if they're chosen.
While the novel suggests that it's an important part of a young person's development to learn to question people and books, the way that Dumbledore talks about the Goblet of Fire suggests that the things that are exempt from this kind of questioning are magical objects like the Goblet and Harry's Sneakoscope in the previous novel. In this way, these magical objects come to act as outside observers and markers of right and wrong, given that the Goblet's entire purpose is to choose the worthiest candidate from each school.
Fred and George scoff at the Age Line and discuss using an Aging Potion. They ask Harry if he'll try to get in and Harry wonders if Dumbledore would be angry if someone younger managed to fool the Age Line. Ron scans the crowd looking for Krum and sees the Durmstrang students heading back to their ship. Karkaroff offers Krum mulled wine and snaps at another student who asks for some. Harry steps aside to let Karkaroff through the door first, but Karkaroff stops to stare for a moment. From behind them, Moody growls that it's Harry Potter and when he sees Moody, Karkaroff looks scared and angry. Karkaroff sweeps his students away.
The way that Karkaroff treats Krum and his other student who asks for mulled wine indicates that he's unashamed about playing favorites and doing so openly. This shows that he's unconcerned with treating his students equally and as though they're all people worthy of attention and instead, focuses his attentions on those who are already especially powerful. This is confirmed when Karkaroff fixates on Harry here; Harry is famous like Krum is.
The next day, Saturday, most students eat breakfast early and admire the goblet, which is surrounded by a thin gold line. A third year girl says that everyone from Durmstrang has put in their name but she hasn't seen anyone from Hogwarts. Harry notes that if he were putting his name in, he'd do it at night so nobody would see. Hearing a laugh, Harry turns and sees Fred, George, and Lee coming down the stairs having just taken their Aging Potions. Hermione warns them that Dumbledore would've thought of this, but Fred jumps over the line. George joins him and a moment later, the twins are ejected from the circle and sprout long beards. Everyone, including Dumbledore, laughs.
Hermione's comment that Dumbledore would've put precautions in place against Aging Potions shows that even as she's learning to question authority and authority figures, she still trusts Dumbledore to follow through on his word and protect his students. Dumbledore's sense of humor about Fred and George's attempt shows that though he has the power to punish them, he understands how important this could be to them and wants them to know that trying isn't a crime.
In the Great Hall, Harry, Ron, and Hermione discuss with Dean and Seamus that Cedric Diggory and the Slytherin Quidditch captain put their names in. They see Angelina Johnson, a Gryffindor Chaser, looking embarrassed. She tells the table that she just had her birthday and so put her name in.
When the students discuss who of their number should be the Hogwarts champion, it creates an environment in which they're asked to make judgments about each other and don't have to be kind to their classmates.
Harry, Ron, and Hermione decide to visit Hagrid, and Hermione runs upstairs to get her S.P.E.W. badges. As Harry and Ron wait, they watch Madame Maxime supervise as all her students submit their names. Hermione arrives in time for the trio to follow the Beauxbatons students back to their carriage. When Hagrid answers the door, Hermione is dumbfounded: Hagrid is wearing his best suit and has his bushy hair slicked down. He happily tells them that the skrewts are now three feet long and starting to kill each other, so he only has 20 left.
Hagrid's groomed appearance indicates that, though he's an adult and has already undergone puberty, he's embarking on a similar journey to the trio’s: it's implied that he's romantically interested in Madame Maxime. By exploring how Hagrid handles these feelings going forward, the novel is able to show that some of the struggles of puberty don't end there and actually continue into adulthood.
As Hagrid makes tea, they discuss the Triwizard Tournament. Hagrid knows what the first task will be, but he refuses to say. Harry, Ron, and Hermione stay through the afternoon and Hagrid refuses Hermione's request that he join S.P.E.W. He insists that it'd be unkind to free elves and insulting to pay them. When she offers Dobby as an example of what she's trying to do, Hagrid notes that Dobby is strange. Finally, around five o'clock, they decide it's time to head to the feast. Hagrid puzzlingly puts on cologne before they go and then leaves the trio to walk up with Madame Maxime.
Again, just as with Percy and Ron, Hagrid's refusal to join S.P.E.W. likely stems from the fact that he has little reason to free individuals he benefits from, though it's also telling that he gives Hermione a reason from the house-elves' perspective. By insisting that it would be unkind and insulting for S.P.E.W. to achieve its aims, he underhandedly encourages Hermione to work with the house-elves, not for them in this manner.
When the feast is over, Dumbledore gets to his feet and explains that when the goblet chooses, the champions should proceed to a small room off the hall. The goblet's flames turn red and a piece of parchment flutters into Dumbledore's hand. He announces that Viktor Krum is the Durmstrang champion. A moment later, he reads that Fleur Delacour will be the Beauxbatons champion. Finally, he says that Cedric Diggory will represent Hogwarts. Dumbledore starts to address the remaining students, but the goblet turns red again and spits out one more piece of parchment that reads, "Harry Potter."
The simple fact that the impartial judge deems Cedric Diggory the most worthy candidate among all Hogwarts students tells the reader that, though Ron thinks little of Cedric, the reader should be open to the possibility that Cedric has more to offer than previously thought. When Harry's name comes out, it shows that even this impartial magical object can be fooled and isn't entirely trustworthy.