At what point in time is this novel set, and how can you tell? Cite textual evidence to explain your answer.

There's no definitive answer to this question. All we know for sure is that the story is set some time in the future. However, with a little detective work, we can set the story at or around 2053, exactly one hundred years after Fahrenheit 451 was published.
In the novel, Clarisse mentions that her uncle was arrested one time for being a pedestrian. This is arguably a reference to "The Pedestrian," a short story written by Ray Bradbury, which he said was a prequel to Fahrenheit 451. Indeed, in an interview, Bradbury explicitly stated that "The Pedestrian" is the beginning of Fahrenheit 451. As "The Pedestrian" is set in the year 2053, we can reasonably conclude that Fahrenheit 451 is set around that time or possibly not long after.

The exact date is not specified, but Fahrenheit 451 is set at least 40 years after it was published in 1953. There are three allusions to a period after 1990 or later.
One mention of time is by Montag, when he speaks in frustration about war and the dim hopes for peace.

We've started and won two atomic wars since 1990!

Another place in the book where time is mentioned is toward the end, indicating a setting in at least 1995. Granger is telling Montag about his grandfather, who had shown him films 50 years earlier of the effects of the V-2 rockets and of the atomic mushroom cloud. The V-2 was the rocket with which Nazi Germany bombarded London and other targets beginning in 1944. The first atomic bomb was dropped by the U.S. in 1945.