A simile is a comparison that uses the words like or as.
Similes are often used in this story by Bradbury, a lyrical writer who infuses a poetic sensibility into his prose. An example is as follows:
There was a sound like a gigantic bonfire burning all of Time, all the years and all the parchment calendars, all the hours piled high and set aflame.
I don't have page numbers (and likely wouldn't have the same edition as you anyway), but the quote above is six paragraphs into the story, near the beginning. As Eckels enters the time travel office, he hears the sound of the time machine. He compares the sound—and the colors he sees—to a bonfire burning up time. It is a powerful simile because we can paint a visual and audio picture in our minds of calendars crackling in the flames. This is a concrete way of referring to going back in time to the dinosaur age, but it is also an ominous, dangerous simile, foreshadowing that what is burnt up can't be recovered.
A second simile is as follows:
He could feel them moving there, beyond the walls, almost, like so many chess pieces blown in a dry wind ....
This quote is near the end of the story, about twelve paragraphs up from the end. It is the last sentence in the long paragraph shortly before Eckels sees the sign with the altered spelling. In this simile, Eckels has an eerie sense of foreboding before he realizes fully that history has changed. He thinks of the people outside of the building as chess pieces, objects moved around by forces larger than themselves.