How is Robert Frost's poem "The Road Not Taken" autobiographical?

The poem does not relate to Frost in the sense that it is a first-person narrative about a personal choice that he had to make for himself. Its autobiographical nature is rooted in the fact that Frost wrote it for friend and fellow poet Edward Thomas, who was known for his inability to make decisions. Frost essentially wrote the poem to mock his friend who had written "Roads," a similar poem about historical pathways which had been constructed by the Romans in his home country, Wales. Many of these roads were still being used, and Thomas wrote about both the literal and metaphoric significance of these routes.

In her article, "Robert Frost : 'The Road Not Taken,'" Katherine Robinson says the following:

Robert Frost wrote “The Road Not Taken” as a joke for a friend, the poet Edward Thomas. When they went walking together, Thomas was chronically indecisive about which road they ought to take and — in retrospect — often lamented that they should, in fact, have taken the other one. Soon after writing the poem in 1915, Frost griped to Thomas that he had read the poem to an audience of college students and that it had been "taken pretty seriously… despite doing my best to make it obvious by my manner that I was fooling… Mea culpa.”

She further also states,

shortly after receiving this poem in a letter, Edward Thomas enlisted in the army and was killed in France two months later. 

When Frost sent the poem to Thomas, Thomas initially failed to realize that the poem was (mockingly) about him. Instead, he believed it was a serious reflection on the need for decisive action. (He would not be alone in that assessment.) 

Frost was disappointed that the joke fell flat and wrote back, insisting that the sigh at the end of the poem was “a mock sigh, hypo-critical for the fun of the thing.” The joke rankled; Thomas was hurt by this characterization of what he saw as a personal weakness — his indecisiveness, which partly sprang from his paralyzing depression.

To clarify the point even more, the author also states, in simpler terms, the following detail:

when Frost and Thomas went walking together, Thomas would often choose one fork in the road because he was convinced it would lead them to something, perhaps a patch of rare wild flowers or a particular bird’s nest. When the road failed to yield the hoped-for rarities, Thomas would rue his choice, convinced the other road would have doubtless led to something better. In a letter, Frost goaded Thomas, saying, “No matter which road you take, you’ll always sigh, and wish you’d taken another.” 

Frost, after the poem had been published, was constantly questioned about its cryptic nature and he often commented that the poem was "tricky." This obviously implied the poem should not be taken at face value, as his friend had, unfortunately, done. It has greater meaning and depth.