Maybe you want to hear about the brother's adventures in Belgium but, no, we're stuck with the narrator and the curate. And they're stuck, too – trapped in a ruined house while the Martians are just outside. Through a little peephole, the narrator and the curate can see the crater and the cylinder and the work going on there.
There is a tripod guarding the hole, but that's old news – who hasn't seen a tripod by now? More interesting are the other machines that the narrator describes, especially the handling-machine, which looks like "a sort of metallic spider with five jointed, agile legs, and with an extraordinary number of jointed levers, bars, and reaching and clutching tentacles about its body" (2.2.6).
The handling-machine moves so much like a living animal that the narrator has to remind himself that it's a machine and that the living creature is the Martian controlling it.
Wells takes a moment here to do something that we're not sure we've ever seen before: through the narrator, Wells criticizes the illustrator of his own book. That is, the narrator notes that he saw illustrations of the tripods that made them look stiff and boring, totally unlike what they're really like (2.2.8).
This is almost definitely a reference to an early magazine publication of The War of the Worlds (in Pearson's Magazine) that had illustrations that Wells was not happy with. They are pretty cheesy. Here's an illustration of a tripod from the original magazine publication.
The narrator takes this opportunity to observe the Martians closely. They disgust him less now, but he finds them "the most unearthly creatures it is possible to conceive" (2.2.10). To which we want to respond, "duh, they're unearthly because they're not from Earth."
Anyway, according to the narrator, the Martians are just heads and tentacles (which serve as hands). They have no nose and (as a later dissection revealed) no guts.
In fact, they don't eat like we do, but instead inject blood from other creatures directly into their own veins. That may sound horrible to us, but let's think what an intelligent rabbit would feel about our meat-eating habits, says the narrator (2.2.13).
In fact, injecting blood means they are free from all sorts of work digesting their food and all of the mood swings that come with being hungry or full. (And this is the narrator telling us about mood swings, so he really knows what he's talking about.)
The narrator also notes that the Martians have probably attacked humans because their usual food was some Martian creature that looked vaguely human.
The narrator also takes this opportunity to provide three big differences between humans and Martians: 1) the Martians don't sleep; 2) the Martians don't have different genders – they're really just big brains with hands; and 3) the Martians have no microorganisms.
But rather than talk about that last part (which is surely not important), the narrator wants to tell us about the red weed, which is an invasive plant species that spreads everywhere very quickly.
(For an example of real-life invasive plant species, check out the famous is kudzu, a.k.a. "the vine that ate the South.")
As the world's leading expert on Martians, the narrator also wants to tell us that he thinks they communicate through telepathy. The Martians do make sounds, but those are just sounds, not language of any kind.
And lastly, the narrator remarks that the Martians don't wear clothes (which is utterly scandalous in Victorian Britain), but the Martians do have a lot of technology that they "wear." "They have become practically mere brains, wearing different bodies according to their needs just as men wear suits of clothes and take a bicycle in a hurry or an umbrella in the wet" (2.2.25).
The narrator then makes the connection between people and Martians super clear: "We men, with our bicycles and road-skates, our Lilienthal soaring-machines, our guns and sticks and so forth, are just in the beginning of the evolution that the Martians have worked out" (2.2.25).
The curate wants to spy on the Martians too, so the narrator has to give up the peephole for now.