Prose writers shouldn't have all the fun of storytelling. Sure, essays, short stories, and novels are where we expect to find stories, but poems also can tell stories effectively. From the earliest epics, right up to the present day, people have built poems from stories--sometimes fictional, sometimes true. Gary Snyder's "Hay for the Horses" is a poem that tells a story, as are William Stafford's, "Traveling Through the Dark," Robert Frost's "Out, Out--," and William Wordsworth's "Strange Fits of Passion I Have Known."
Besides presenting vivid incidents, settings, and characters, stories can provide a sense of structure and purpose. To get started on a story poem, begin by quickly writing down a sequence of events from beginning to end. Then add some details, some characters, some tension, some suspense. For more storytelling suggestions, see Writing a Story in Paradigm Online Writing Assistant.
For this poem, try one of the following:
1) Write about something that happened within the past week. This doesn't have to be a major, life changing event. Maybe you had to change a flat tire. Or perhaps you watched your pet snake shed its skin. Maybe you gave your garage a long overdue cleaning. The event itself doesn't matter so much as your telling of it. Just start right in and write through a quick draft to get started.
2) Write about something that happened at least five years ago. Pick an event you've had time to reflect on, something that stands out now as playing an important part in who you are today. As you write, don't tell why this event is important, just concentrate on getting your reader into the feel of actually being there. Provide plenty of concrete, specific details to make the story come alive.
Whichever of the above options you choose, keep the poem short, compressed, to the point--no more than 24 lines as an absolute maximum. You may want to write this out first as prose, then add line breaks and stanza breaks when you complete your first draft.