I'm working on a project of narrative poems these days, so different from the lyric poems I generally write. There's a reason I want a narrative thread to my current project, and there are new challenges that come with it. The one I'm struggling with now is prose-iness (prosiness, prosyness, however you want to spell it).
I've found a few things helpful. Here are notes to myself:
1) Pursue constant persistent editing. Pull out anything that isn't necessary, and there will be more of it than there is in lyric poems. This is a difficult balance though, because more explication is necessary than in lyric poems, and yet you want as little as possible. How to decide? Look at the next tip.
2) Get rid of anything that doesn't advance the poem emotionally. If it advances the narrative but not the emotion, cross it out. Then if the narrative has become too sketchy, try again to add what detail you need, but remember the new line(s) must advance the poem emotionally or they will end up getting cut.
3). FORM! I have often lamented my tendency to write little bricks of poems, all left-aligned and stanza-y. Cutting out as much as I could from a narrative poem left me a stack of sickly little bricks that I hated. But then I teased them out--spread the words across and over lines, indented some lines, used physical space to show where I had left out a part of the story it was my natural tendency to keep in, but that persistent pruning had convinced me to cut out. And then that missing bits didn't bother me anymore--the passage of time, the elliptical suggestion of missing elements there in the form left room for the missing parts without even having to mention them.
And now I had a poem that wasn't all brick-like and typical of me. Success with a narrative poem!