Read examples of both nonsense and narrative poems. Reading can often be an important and inspiring part of writing. Lewis Carroll's poem "Jabberwocky" is a fitting example of a nonsense narrative poem. This poem invokes ridiculous characters, strange words and phrasing, yet attempts to tell a story.
Begin by brainstorming ideas. Think of a few characters you want to introduce, as well as plotlines. Since this will be a nonsense narrative, don't worry about "making sense" and being specific about your ideas. When brainstorming, you can jot down phrases, lines, or even draw scenes and characters.
Start your poem with a broad opening, such as setting a scene. Consider how much time you want to spend on the poem's opening, especially if this will be a longer poem. Again, since this is a nonsense poem, do not worry about "making sense" or logistics. Be creative, silly and open with your ideas.
Introduce a ridiculous conflict to help your narrative along. This conflict should be humorous and nonsensical and pertain to your characters. Don't worry about following a linear timeline, since a nonsense narrative can be fragmented. As "nonsense," this conflict doesn't need to be resolved.
Add lots of jokes and puns throughout. Humor is important for nonsense poems. Be absurd, use word play or use incorrect grammar. You can even make up your own words!
Follow your ear when writing. In other words, play with rhymes, slant rhymes and alliteration. Sound play will add to the whimsical nature of your poem and create a rhythm. If you feel like you're stuck on a line, try writing by association. If you write "mouse," you might jump to the word "cheese" or even "moose" because of the sound association.