Harry, Ron, and Hermione bundle up and cover themselves in the Invisibility Cloak to walk to Hagrid's. They pass Nearly Headless Nick humming "Weasley is our King" and shuffle through the snow. Hagrid lets them in and Hermione screams at the sight of Hagrid: his face is bruised and cut, and his hair is matted with blood. Hagrid refuses to say what happened, makes tea, and slaps a greenish steak onto his face. He says it's a dragon steak and helps the stinging of his wounds. Hermione asks if the giants beat Hagrid, and Hagrid angrily accuses them of being nosy. He admits that he did see the giants and agrees to tell the story when Ron and Harry offer to tell Hagrid about Harry's dementor attack in return.
In Hagrid's case, the trauma he clearly experienced at the hands of the giants is more physical than emotional, yet the happiness and pleasure he goes on to take in telling the story supports the novel's assertion that telling one's story can be cathartic. Further, the draw of being able to tell Hagrid about Harry's attack shows Harry that he has another ally in the school who will believe him—and judging by Hagrid's willingness to talk, won't ignore him.
Hagrid sighs and says that he and Madame Maxime set off after school ended the previous year and traveled for a month to get to the mountains where the giants are. It took so long because the Ministry was following them. They found the valley where the giants were hiding, and there were only about 80 of them. They walked down into the camp toward Karkus, the Gurg (chief), with a gift of everlasting fire held over their heads. Karkus didn't speak English, so he called some giants who did know English to translate. Hagrid and Madame Maxime said they came on Dumbledore's behalf and would return the next day with another gift.
By taking things slowly with the giants and making it clear that they're not visiting to make trouble, Hagrid and Maxime try to show the giants that they respect them and understand that this is something that the giants will have to choose independently—Hagrid and Maxime can't and won't force them to fight for Dumbledore. By showing them this respect, it's more likely that the giants will be receptive to the message.
The next day, Hagrid and Maxime gave Karkus a goblin-made battle helmet and Karkus seemed interested in Dumbledore's message. That night, however, a brawl broke out among the giants. Karkus was dead in the morning, and a giant named Golgomath was the new Gurg. Golgomath wasn't interested in talking and tried to hurt Hagrid, so Maxime cursed Golgomath and they ran. They spent the next few days watching Golgomath speak to Death Eaters. They then checked caves to find giants who might be sympathetic to Dumbledore and they found several who were interested. Golgomath found and killed those giants a few days later, and now, no giants are coming to help the Order. Hermione asks about Hagrid's mother, and Hagrid gruffly says that she died years ago.
Because Dumbledore doesn't have any power at the Ministry right now, it's possible he can't promise giants anything substantial like the Death Eaters, who wish to control the Ministry (and by extension, the offices that control what giants can and can't do under Wizarding law), can. The Death Eaters may simply be able to offer more at this point because they're better connected. This should impress upon Harry the importance of spreading the word of Voldemort's return, as Dumbledore's side is quickly losing allies.
Before Hagrid can try to explain his injuries, someone knocks on the door. Harry sees Umbridge's shadow, sweeps the Invisibility Cloak over Ron and Hermione, and hisses for Hagrid to hide their mugs. Hagrid lets Umbridge in and she rudely introduces herself. She asks about the footprints leading to Hagrid's door and Hagrid feigns ignorance. Umbridge searches Hagrid's cabin, asks about his injuries, and asks where Hagrid has been. Hagrid's excuses are feeble, and Harry believes that Umbridge knows that Hagrid has been in the mountains. As Umbridge leaves, she tells Hagrid to expect an inspection and threatens to fire him.
Umbridge is automatically biased against Hagrid both because she knows he’s close to Dumbledore and he’s a half-giant. Given her previously expressed dislike of “half-breeds,” she sees him as less-than because of his heritage, and also wants to use him to gain information about Dumbledore. Unfortunately, Hagrid has never been very good at lying or keeping secrets.
When they're sure Umbridge is gone, Harry, Ron, and Hermione throw off the cloak and Hermione tries to convince Hagrid to show them boring creatures in class that won't offend Umbridge. He happily refuses and says he has a good surprise planned for his first class. Hagrid tries to sooth Hermione and then shows the trio out of his cabin. Hermione erases their footprints as they walk and vows to plan Hagrid's lessons to protect him from Umbridge.
Because Hagrid has been gone and doesn't know how horrible Umbridge is yet, he isn't in a place to take Hermione's warnings seriously and compromise his own desires for the sake of his job.