No infallible advice can be given on how to write a poem, because poets develop their own approaches in time. Nonetheless, here are a few exercises to generate the raw copy.
How much time is available? Opening lines can be dashed off in minutes but completion may take days or weeks. Be cautious, and aim perhaps for 5-10 lines in an evening. Don’t wait for the muse, but write what you can when you can. Odd phrases and lines are at least something to work from, and more inspiring than a blank page.
When you write letters or tell stories, do you usually start from a newspaper article you’ve read, an anecdote told or overheard, something witnessed, a general reflection? Start a poem in the way you’re most comfortable with.
What sort of poem had you in mind? A story, a comment, a tribute, a protest, an elegy, a character study, a memorial? Skim through contemporary examples to start yourself off.
About the issues involved. Imagine the poem were a newspaper article: what points would you make, with what evidence and resounding arguments? Got it together? Go on then: let yourself go. Something will emerge.
Automatic writing. Say 5 minutes at a stretch, continuously, never stopping. Go through the material when you’ve collected in ten pages or so, and circle anything interesting.
Get a friend to say words at random. Write down the first response that comes to you. Build a poem around three of the words.
Open a diary or journal (yours or someone else’s) and jot down the first incident on three successive pages. Make a poem of these.
Describe, as closely as you can, some recurring dream or nightmare. Reverse the sequence, and then make a poem.