Poetry with rhyme and meter was the standard in poetry for centuries before modern poets in the early 1900s, then modernists, began writing poetry in prose form. While writing of any kind should be grammar- and spelling-accurate, there are many rules in writing that can be broken with artistic license to help convey the ideas of the writer. Prose poetry began as a way to break the rules established by traditional poetry and is now the freest way for poets to put their thoughts on paper.
Choose a subject. While your poem does not have to project a moral to a reader, it should say something. Pick a topic that makes you feel something or that you have an opinion about and reflect your thoughts in your poem.
Outline a strategy. How are you going to reflect your thoughts? If you plan to use the helpful tool of figurative language, jot down the metaphors, similes, images, allegory or whatever tool you plan to use before you begin writing your poem so that you have a clear picture of how that device can be used within your poem.
Decide how you'll structure your poem. This can change after you've written your first couple of drafts, but choosing things like stanza length and line length will contribute to how succinct or detailed your voice will be, though in a prose poem, these things can change at your leisure. Also decide what you'd like the spine of your poem to be. The spine is the final word in each line extending throughout the poem. While readers will not stop reading at the final word in each line, those words will leave an impression on the reader's eye.
Write your first draft. Forget the rules in form you learned with rhyming and metered poems; this poem can have whatever form you decide for it. The most important part of writing the first draft of a prose poem is to experiment. Writing a poem is not like writing a book; it's a short process with many expected rewrites that don't take an overwhelming amount of time. Try things. You can always get rid of them.
Set your poem to the side. The tendency for writers is to want their product to be finished as soon as the first draft is completed. Few parts of this process are as important as ignoring your poem for a while -- for days, even -- and returning to it later with a fresh perspective on your work.
Read the first draft of your poem. Decide if the material with which you experimented actually worked. Your poem may be prose, but it is still a short piece, so tighten up your work where you can. Avoid superfluous text. The tighter a poem is, the more a reader is likely to read it to the final word.
Show your poem to a peer. After they've read, ask them if they immediately noticed some of the ideas you attempted to portray through figurative language. Complete this step with an open mind; not everyone is going to love your work.
Edit your poem until you feel comfortable with a finished product. You will likely need to make a few adjustments, then spend a couple of days away from it, and repeat this process until you return to your poem and there are no adjustments you see necessary.