The War of the Worlds tells one major story (Martians invade!), but it tells this story through a few vantage points. For instance, most of the book is about the narrator's adventures, but then several chapters are about the narrator's brother's adventures, and a few paragraphs go up to a bird's-eye view of the situation, as if all of humanity (or at least all of England) were the protagonist. In some ways, we could say that the narrator's story and the narrator's brother's story are two varieties of the same story – the "aliens land, what do you do?" sort of story. Keep that in mind while we sketch out a basic plot analysis.
There's a lot of preamble in the first chapter, but the story basically starts with the Martian cylinders landing and people becoming curious about them. All the best stories start with aliens landing. Actually, if we could be serious for a moment – just a moment, we promise – we might say that a lot of stories begin with some strange, unexpected event that interrupts the people who are going about their ordinary days. Now, this could be Book 1, Chapters 1-3 for the narrator's story, and the beginning of Book 1, Chapter 14 for the narrator's brother's story. In both of these stories, the aliens have arrived, but we don't know what they're going to do.
In a book titled The War of the Worlds, the main conflict may be when the worlds start fighting each other. This part begins slowly, with the Martians revealed as different and disgusting, but pretty soon it's all Heat-Rays and Black Smoke. There's not a lot of ambiguity going on here: this is conflict, Martian-style.
But let's also take a totally different view. Since the narrator is our most important character, what's his main conflict? After all, although he's affected by the Martian invasion, he's not directly fighting them. Well, we might want to say that he's torn between different feelings. For instance, when the Martians emerge from the first cylinder, he's both afraid of them and curious. He describes himself as a "battlefield" between these two emotions (1.5.1). When the Martians attack, he wants to fight them and get his wife to safety. We might say that he's in a conflict with himself.
In many other books, this would be the climax: a war starts and your side loses. But in The War of the Worlds, this is just a complication. For the narrator and his brother, the army's loss against the Martians basically means they have to get the heck out of town. As they run, they pick up some companions. That is, the narrator picks up the artilleryman and then the curate, while the narrator's brother picks up the Elphinstones. Now, when you're trying to run away and hide, meeting someone new can be a real complication. For one thing, now you have to find a place big enough to hide you and your traveling companion.
The narrator and his brother are trying to survive, which means either hiding or running (or both) from the Martians. In the brother's story, his adventures reach a turning point when they board a ship headed for Ostend. If you were holding your breath for the brother's fate, now's the time for you to let it out.
Unfortunately for him, the narrator has a less happy climax to his story. After being stuck in the ruined house with the curate, they begin to fight. First they argue over who gets to look through the peephole, then over the limited supply of food, and finally over the curate's desire to confess out loud. And after days of bickering, the narrator attacks the curate with the blunt end of a meat cleaver. Hitting someone with a meat cleaver might only be self-defense, but still, it's a heck of a climactic turning point.
Even though the narrator is hiding in a coal cellar all alone, and the narrator's brother is on a ship headed for Ostend with the Elphinstone family, both of them are facing the same question: will the Martians get us? The tripods are wading out to sea to get the brother, while the handling-machine is feeling inside the house where the narrator is hiding to see what it can find. Dun dun DUN!
In some ways, the Thunder Child scene is so exciting we're tempted to call it a climax, since climaxes are usually exciting. But since we're using "climax" here to mean "turning point," the Thunder Child scene is more of a denouement – we get to see how the results of the climax unfold. In the denouement, the brother and other people boarded ships, the Martians came after them, and then the Thunder Child destroys the Martians (and maybe is destroyed by the Martians).
As for the narrator, he leaves the ruined house, only to discover that the world has totally changed. He's been hiding in the ruined house for two weeks, after all, and in that time, the Martians have pretty well taken over. At least, that's what it looks like, with the red weed everywhere.
We don't really have to say much about the brother's conclusion because it's all happy and heroic. As for the narrator, his story ends when he discovers that the Martians are dead and his wife is alive. In many other books, this would be the climax. (And it kind of is a climax here, which makes, what, three or four climaxes? This book is a little unusual in its structure, so it doesn't always fit so well into a classic plot mold.) But after 168 pages (in our copy) of Martians attacking, these final 12 pages go so quickly that it feels more like a conclusion than a climax. In fact, it rushes through so many different topics – Martians dead, wife alive, Earth doing fine, but for how long? – that it reminds us of those epilogues in movies that tell us how every one is doing after the big climax.
Or, hey, maybe the real conclusion is when the narrator thinks that we might invade Venus. That's not the lesson we got from the book, but maybe that's the lesson we're supposed to get. It's hard to say because the ending is so open-ended.