Section I (Lines 1-8) Summary

Get out the microscope, because we’re going through this poem line-by-line.

I met a traveller from an antique land
Who said...

The poem begins immediately with an encounter between the speaker and a traveler that comes from an "antique land."
We're not sure about this traveler. He could be a native of this "antique" land, or just a tourist returning from his latest trip.
We don't know where this encounter is taking place; is it on the highway? On a road somewhere? In London? Maybe if we keep reading we'll find out.
"Antique" means something really old, like that couch at your grandmother's or the bunny ears on top of your television. The traveler could be coming from a place that is ancient, almost as if he were time-traveling. Or he could just be coming from a place that has an older history, like Greece, Rome, or ancient Egypt.

…Two vast and trunkless legs of stone
Stand in the desert. Near them on the sand,
Half sunk, a shatter'd visage lies…

Here the traveler begins his speech. He tells the speaker about a pair of stone legs that are somehow still standing in the middle of the desert.
Those legs are huge ("vast") and "trunkless." "Trunkless" means "without a torso," so it's a pair of legs with no body.
"Visage" means face; a face implies a head, so we are being told that the head belonging to this sculpture is partially buried in the sand, near the legs. It is also, like the whole statue, "shatter'd."
The image described is very strange: a pair of legs, with a head nearby. What happened to the rest of the statue? War? Natural disaster? Napoleon?

…whose frown
And wrinkled lip and sneer of cold command
Tell that its sculptor well those passions read

The traveler now gives a fuller description of the "shatter'd visage" lying in the sand.
As it turns out, the "visage" (or face) isn't completely "shatter'd" because one can still see a "frown," a "wrinkled lip," and a "sneer."
We still don't know whom this statue represents, but we do know that he was upset about something because he's frowning and sneering. Maybe he thinks that the sneering makes him look powerful. It conveys the "cold command" of an absolute ruler. He can do what he wants without thinking of other people. Heck, he probably commanded the sculptor to make the statue.
After briefly describing the "visage" (3), the lines shift our attention away from the statue to the guy who made the statue, the "sculptor."
"Read" here means "understood" or "copied" well. The sculptor was pretty good because he was able to understand and reproduce exactly – to "read" – the facial features and "passions" of our angry man. The sculptor might even grasp things about the ruler that the ruler himself doesn't understand.
The poem suggests that artists have the ability to perceive the true nature of other people in the present and not just in the past, with the benefit of hindsight.
"Tell" is a cool word. The statue doesn't literally speak, but the frown and sneer are so perfectly rendered that they give the impression that they are speaking, telling us how great the sculptor was.

Which yet survive, stamp'd on these lifeless things,
The hand that mock'd them and the heart that fed

The poem now tells us more about the "passions" of the face depicted on the statue.
Weirdly, the "passions" still survive because they are "stamp'd on these lifeless things." The "lifeless things" are the fragments of the statue in the desert.
"Stamp'd" doesn't refer to an ink-stamp, but rather to the artistic process by which the sculptor inscribed the "frown" and "sneer" on his statue's face. The word could also make you think of the ruler's power. Had he wanted to, he could have stamped out any of his subjects who offended him.
"Mock'd" has two meanings in this passage. It means both "made fun of" and "copied," or "imitated." "Hand" is a stand-in for the sculptor. So the sculptor both belittled and copied this man's passions.
"The heart that fed" is a tricky phrase; it refers to the heart that "fed" or nourished the passions of the man that the statue represents. But if you think these lines are unclear, you're right. Even scholars have trouble figuring out what they mean.
The passions not only "survive"; they have also outlived both the sculptor ("the hand that mock'd") and the heart of the man depicted by the statue.
Note the contrast between life and death. The fragments of the statue are called "lifeless things," the sculptor is dead, and so is the statue's subject. The "passions" though, still "survive."