Since we spend a lot of time in Lina's and Doon's heads, we get a sense of how they think of the people around them. Like when Lina goes to see Clary on an errand: "You might have thought from looking at her that she was a gruff, unfriendly person—but her nature was just the opposite… She was strong but shy, a person of much knowledge but few words. Lina had always liked her" (4.38). So we know Lina's opinion of Clary, and we find that it's a generally accurate description once we see Clary in action (she's caring and attentive whenever Lina comes to talk to her, for example).
Sometimes, a simple but direct statement does the trick, and suddenly we have a better idea of who a character is and what drives them. When Lina is trying to decipher the message from the Builders, she suddenly realizes that she should ask Doon because "he was curious. He paid attention to things" (7.98). Bam. There you go. Direct characterization accomplished.
In a city where nothing new is produced, we imagine that clothing is one of the more valuable goods. Sure, people can mend their clothing, and make new clothes out of recycled fabric, but there's no clothing factory as far as we know. Some was kept in the storerooms, but they must be running low by now. So, as we'd expect, most of Ember's citizens are running around in old, ratty clothes.
Doon, for example, is always wearing an old "brown corduroy jacket" (1.6), while Lina, once she gets her red messenger's coat, is rarely seen without it. We begin to associate these clothing items with these characters.
The big exception to this rule is the mayor. In addition to hoarding food and light bulbs (and board games, we'd hope), he's also been hoarding clothes. This shows his lack of foresight—who does he have to look good for, anyway?—and also annoys Lina: "She thought about the mayor, down in his room full of plunder, gorging on peaches and asparagus and wrapping his huge body in elegant new clothes… What was he thinking?" (14.1). We agree: what's up with that, mayor?
How people in Ember act gives us clues as to who they are. We could pick an obvious example—the mayor stealing supplies means he's a selfish person, maybe even evil—but we'll go with a more subtle one.
We've been told again and again that Doon is angry, but we also see his anger manifesting in his actions. Like when he tries to climb a pole as a younger kid (the event that leads to him and Lina no longer being friends):
When he heard Lina and the others laughing, his face darkened. His temper rose in him like hot water. "Don't you dare laugh at me," he said to Lina. "I did better than you did! That was a stupid idea anyway, a stupid, stupid idea to climb that pole…" And as he was shouting, red in the face, their teacher, Mrs. Polster, came out onto the steps and saw him. (2.10)
So yeah. Instead of just writing, "Doon was one angry kid," we get a description of how his actions reveal the angry side of his personality.