After a dinner party, the Time Traveller argues that time travel is possible. Since the narrator calls him "the Time Traveller," and since it's impolite to argue with your host, we're going to go out on a limb and agree with him. The guests mostly don't believe the Time Traveller, though, not even after he makes a model Time Machine disappear and then shows them the full-scale machine.
The following week, the Time Traveller is a half hour late to his own dinner party. This is not only improper from an etiquette standpoint, but also pretty inexcusable if you have a Time Machine. (We're guessing his Time Machine is not so precise.) The guests are astounded at his disheveled look, so he tells them his story.
The Time Traveller has gone far, far into the future – to the year 802,701. He has no guide there, leaving him to make guesses about what's going on. His Time Machine gets stolen, so he has to stay and find it. He meets the beautiful but dumb Eloi, who are like lazy children. His first theory is that the Eloi have machines that do their work for them so they can sit around and be lazy.
He befriends one of the Eloi, a woman named Weena. In every movie adaptation of this book, the Time Traveller and Weena fall in love, but in the book it's not so romantic. We're not sure exactly what's going on between them, though (check out "Characters: Weena" for more on that).
Then the Time Traveller discovers that there are people who live underground. He goes underground and meets them: the creepy Morlocks. The Time Traveller's second theory is that the Morlocks are the helpful workers who take care of the Eloi. In this theory, the Eloi are descended from the upper class, the Morlocks are descended from the working class, and everyone is happy – although the Morlocks are disgusting. (The Time Traveller compares them to Kentucky cavefish, which we think are kind of cute, but we'll give it to him.)
Then he realizes that the Morlocks do take care of the Eloi, but they also eat them. (In case you're wondering, Eloi tastes like chicken.) The Time Traveller also learns that the Morlocks are sensitive to light and afraid of fire.
The Time Traveller examines an old museum to find a weapon to use against the Morlocks. He finds a club, which works as well in the future as it would work now. But the Morlocks attack. The Time Traveller sets a fire, which gets out of control (doh!). He loses Weena but finds his Time Machine.
He travels even farther into the future, when almost all life has died out. It's kind of a bummer, so he goes home.
And that's his story. No one believes the Time Traveller, except the narrator (sort of). The narrator goes to talk to him the next day, and the Time Traveller says he'll be back with proof. The Time Traveller goes into his lab and disappears. He never comes back.