how does the poem Ozymandias make the reader feel?

Readers will respond differently to this poem, but one common reaction would be to experience a feeling of desolation. One might also come away with a sense of the futility of the kind of tyrannous greatness Ozymandias pursued.
The desolation or emptiness one feels in contemplating Ozymandias and his once mighty kingdom emerges through Shelley's imagery. Imagery is description using the five senses of sight, hearing, taste, touch, and smell.
In "Ozymandias," we are left with images of brokenness and emptiness. We can visualize the following:

Two vast and trunkless legs of stone
Stand in the desert

These severed legs with no trunk (torso and body) are all by themselves in the desert. The head of Ozymandias is broken off and lies by the statue's feet as if he has been beheaded. This is an image of destruction and loneliness. Later, we learn the following:


Round the decay
Of that colossal Wreck, boundless and bare
The lone and level sands stretch far away.

Words like "boundless," "bare," "lone," and "level" offer to our mind's eyes a vista of aloneness where once a great kingdom stood. The complete silence of this scene is also desolate.

The words that Ozymandias had carved on his statue are now ironic. He calls on the "mighty" to look on his works and despair. He means for them to see his vast city, his armies, and his wealth and know that they cannot challenge him. Instead, the "mighty" now should despair because such "great" works came to nothing but desert sand. Shelley was a political radical in his time (although his convictions would not seem as radical to us), and he supported the ideals of the French Revolution. The image of Ozymandias's severed head and the "level sands," representing the forces of leveling (a word for equality), are images that warn the powerful of Shelley's day that they too will end up as nothing.

One could certainly feel unsettled after reading Shelley’s sonnet. Essentially an account of a visit to the tomb of Ramses II (the Ozymandias immortalized in the poem), the traveler tells the narrator that all that remains of this once-great king and the civilization he built is a broken statue in the desert. Only the statue’s legs remain upright. On its pedestal, an inscription, once meant to intimidate, is now a grim reminder of the power that time wields over all things: "My name is Ozymandias, king of kings:/Look on my works, ye Mighty, and despair!" Despite the greatness of his works and vastness of his empire, time seems to have mocked the king, as did the sculptor who captured his frown and sneer in the now-ruined stone monument.
Through his work, Shelley alludes to the transience of all man-made things. Even art and language do not survive the ravages of time, which is the only true power. Offering no words of hope, the poem ends abruptly, leaving its reader with only more questions.