Ged goes to Low Torning, which is a town built over many little islands (which is rather beautifully described here).
The town he goes to isn't rich, but Ged grew up among poorer people, so the townsfolk remark that he seems to be without much pride, which – as you'll recall – is a HUGE change for Ged (and something of a relief for us).
Low Torning isn't really important enough for a wizard, but the nearby island of Pendor has some dragons that are beginning to act up. (And it's about this time that we wish someone had made a video game adaptation of this book.)
Ged is happy to be of help, even though Low Torning seems boring. Or maybe he's happy there because it's boring. We're not sure.
The most exciting thing (at first) is that Ged becomes friends with a boatmaker named Pechvarry and his son, Ioethe. Ged learns more about sailing on account of this.
Which makes it a total bummer when Ioethe is dying from a fever.
Pechvarry begs Ged for help. Ged can't help, and the Master Herbal taught him to let dying people go. Pechvarry and his wife really beg, so Ged sends his spirit into the land of the dead, but that doesn't work either. He fails to get Ioethe back and – bonus – he reveals himself to the shadow monster.
Oh, and also he falls into another coma. (Which we think makes three now.)
Ged's otak wakes Ged up by licking his hands and face, which totally teaches Ged that animals have wisdom. Duh.
Since the shadow monster knows where Ged is, he starts having nightmares that interfere with his job (protecting Low Torning against the dragons). He realizes that he can't stay there anymore.
He decides to go fight the dragons on Pendor instead. After all, there are only nine of them.
Actually, several of the dragons are young and dumb, so Ged defeats them, no problem.
But then Ged faces the old dragon. The old dragon is smart and tempts Ged, saying that Ged needs help to face the shadow.
Thankfully, Ged resists the temptation and defeats the dragon by using the dragon's true name, Yevaud. Ged knew that name from reading old legends about dragons.
Since Ged knows Yevaud's true name, Ged gets the dragon to promise to never fly to the other islands. And Yevaud never does (5.91).