Anthony Hecht discusses the origin of his poems in this clip from The Poet's View: Intimate Profiles of Five Major American Poets, which also features Kay Ryan, John Ashbery, Louise Glück, and W. S. Merwin.
I have no advice to offer anyone who wants to be a poet, but I can tell you what W. H. Auden once said in general. He said that if some person came to him and said: "I want to be a poet because I have something very urgent and important to express," the chances are he or she would not be a poet. But if they said instead: "I am interested in putting words together in novel and unexpected ways. I like playing with words, with language," this is someone who might very well turn out to be a poet.
The origins and sources of my poems are many, and of course the most important ones are from personal experiences: the fact that I was a soldier in World War II, that I was one of the first Americans to enter the German concentration camp of Buchenwald. But they come also, of course, from literary sources, from the poets I've admired, both my contemporaries and the great poets of the past, from whom I have learned a great deal. And every once in a while, they come from dreams, of course, too. But also, every once in a while, something comes out of the blue, and I try, if I am able, to take notes on it, to scratch something on the back of an envelope. But if that's impossible, I hope that it will linger somehow or be able to be recalled, and if it can't be recalled I don't worry, because then it probably wasn't important enough in the first place.
A turn, a glide, a quarter-turn and bow,
The stately dance advances; there are airs
Bone-deep and numbing as I should know by now,
Diminishing the cast, like musical chairs.
—from "Sarabande on Attaining the Age of Seventy-Seven"