In a Poets.org interview, poet Cate Marvin says the following in response to the question, "How do you begin a poem?"
I like to think of poets as moving through the world with their minds poised like nets, intent on capturing scraps of language, resonant images. Thinking as a poet means viewing the world as a poem; thus, the poet is prone to existing in real space and time in a most vulnerable manner. This means being super-observant wherever your physical self takes your mind, as it requires being terribly receptive to light, images, movement, conversations between others, oddities many might be inclined to overlook in newspaper headlines, heatedly intimate conflicts overheard in public places, disingenuous directions offered by advertisements and street signs, etc.
Sometimes a poem comes over me like weather, feels like an itch or impulse. It's a near physical sensation. At that moment, there is nothing else to do but move to the typewriter or computer to pound the thing out.
More often, the poem has lived in my head for a long while, and I've battled with the entire idea of it. It insists on being made. I resist. I try and will it away. It won't go away. This is the Real Poem. The poem not born simply out of anger, or from a fit of lyrical bliss—no, this kind of poem has a real agenda. And it happens to me. When I begin this poem, I must be humble. Because this kind of poem, which usually has a big idea in its back pocket, is prepared to duke it out with me for years until I get it right. (By which I mean, one has to write a great many very bad poems to get this kind of poem started.) This kind of poem takes a lot of time. Sitting down. Beginning it again and again. By the point you've started it, it's taken so long to get there, you can't honestly explain to anyone how you began it. It began with you. In you. And it won't quit until you've got it right, by which point it bears no resemblance to the poem you "began."
To read more of Marvin's interview, or to enjoy equally good interviews by Poets.org with poets Gabrielle Calcorvessi and Matthew Dickman, check out the links.