A group of men, including the narrator, is listening to the Time Traveller discuss his theory that time is the fourth dimension. The Time Traveller produces a miniature time machine and makes it disappear into thin air. The next week, the guests return, to find their host stumble in, looking disheveled and tired. They sit down after dinner, and the Time Traveller begins his story.
The Time Traveller had finally finished work on his time machine, and it rocketed him into the future. When the machine stops, in the year 802,701 AD, he finds himself in a paradisiacal world of small humanoid creatures called Eloi. They are frail and peaceful, and give him fruit to eat. He explores the area, but when he returns he finds that his time machine is gone. He decides that it has been put inside the pedestal of a nearby statue. He tries to pry it open but cannot. In the night, he begins to catch glimpses of strange white ape-like creatures the Eloi call Morlocks. He decides that the Morlocks live below ground, down the wells that dot the landscape. Meanwhile, he saves one of the Eloi from drowning, and she befriends him. Her name is Weena. The Time Traveller finally works up enough courage to go down into the world of Morlocks to try to retrieve his time machine. He finds that matches are a good defense against the Morlocks, but ultimately they chase him out of their realm. Frightened by the Morlocks, he takes Weena to try to find a place where they will be safe from the Morlocks' nocturnal hunting. He goes to what he calls the Palace of Green Porcelain, which turns out to be a museum. There, he finds more matches, some camphor, and a lever he can use as a weapon. That night, retreating from the Morlocks through a giant wood, he accidentally starts a fire. Many Morlocks die in the fire and the battle that ensues, and Weena is killed. The exhausted Time Traveller returns to the pedestal to find that it has already been pried open. He strides in confidently, and just when the Morlocks think that they have trapped him, he springs onto the machine and whizzes into the future.
The Time Traveller makes several more stops. In a distant time he stops on a beach where he is attacked by giant crabs. The bloated red sun sits motionless in the sky. He then travels thirty million years into the future. The air is very thin, and the only sign of life is a black blob with tentacles. He sees a planet eclipse the sun. He then returns, exhausted, to the present time. The next day, he leaves again, but never returns.
I think it's important to realize that when the time traveller leaves in the end, he has with him a bag and a camera, so the reader can infer that he will return with proof.