I figured that Tenzin would know the basic details of the war just because of who his family is, but I guess he has to find out some time.
Of course, he isn't told all of the details of the war, but he's most likely told a lot about it now.
Tenzin doesn't learn of the Hundred Year War until he is eight.
Of course, he had heard the basic details and snippets of talk of it on the streets—"I'll say, the Fire Nation hasn't been the same since the war's end," you think you have it bad? I served in the Hundred Year War, and you don't hear me complaining!"—but never the genocide of his father's (and his) people, never the killings, his parents' close calls with death, the reason for Uncle Zuko's scar and the man who gave it to him.
It's not until he hears a harsh gasp resonate through the house from his parents' room that he learns anything about it.
He stands outside his parents' room, his father's back to him. Aang sobs into the shoulder of his mother, who rubs his back soothingly and murmurs, "it's okay, sweetie, it's okay. We're safe; it was just a dream. We're okay," repeatedly. The sobs become more infrequent, and Katara kisses the top of his head and exhales. "Do you want to talk about it?"
Aang nods. "Sure."
Tenzin's mother gives his father a small smile, taking his hand. But it isn't until she and Aang get out of their bed that they notice Tenzin standing in the doorway. "Come on, I'll make you some tea. We don't want to wake the—Tenzin!"
Aang stares at his son for a moment, eyes wide, then relaxes slightly, sitting down on his knees in front of Tenzin. He puts a hand on his shoulder. Tenzin notices that it's still trembling. "When did you wake up?"
Tenzin stares back at his father. "Well, I heard you, and I thought you were in trouble..."
Aang smiles, warm and reassuring. "No trouble, son. I just a bad dream, that's all."
"What was it about?" Tenzin asks innocently.
His parents share a fervent glance at each other, then Aang looks back to Tenzin and sighs. His expression softens. "Well, I guess now is as good a time as any, Katara." He takes Tenzin's hand and starts to lead him down to the kitchen. "How much do you know about the Hundred Year War, Tenzin?"
And with that, Aang and Katara tell him all that they can bear to reveal to him about the war at his age, at about two in the morning over a pot of jasmine tea.