It's a little tricky to identify irony in Ray Bradbury's "The Pedestrian," but there are a few interpretive claims you might make if you need to identify that particular literary device.
Situational irony occurs when the opposite of what we'd expect happens in a particularly interesting or critical way. For example, it would be situationally ironic if the firehouse (the building belonging to the people whose job it is to put out fires) burned down.
You might argue that it's ironic that Leonard Mead continually thinks of the urban landscape he wanders in natural terms:
The street was silent and long and empty, with only his shadow moving like the shadow of a hawk in mid-country. If he closed his eyes and stood very still, frozen, he could imagine himself upon the center of a plain, a wintry, windless Arizona desert with no house in a thousand miles, and only dry river beds, the streets, for company.
Mead's thoughts paint a picture of a city being reclaimed by nature, with sidewalks "vanishing under flowers and grass." He uses this to emphasize the lack of a human presence in the city at night; people sit at home and watch television instead of going out or visiting friends. This is ironic because in Bradbury's vision, the industrialized, technological future actually leads humans to abandon their environment and make less of an impact on the landscape—the opposite of what we might expect. In short, our expectations about what progress should look like are reversed; this vision of progress looks like decline. By the same token, humanity's unnatural technological advances actually cause nature outside to flourish (the opposite of what we would predict).
It’s also ironic that the man we as readers identify as the most normal character in the story—the one who doesn’t want to sit at home and watch TV every night—is regarded by his society as deviant to the point of criminality: at the end of the story, he is taken away to the “Psychiatric Center for Research on Regressive Tendencies.” Though we regard Leonard Mead as natural (both in his behavior and in his affinity with the natural world), his society sees him as unnatural—the exact opposite of what we might expect.