Choose a subject for your poem, and decide on the treatment of the topic. For example, if you choose to write about a historic figure, then you should also decide whether you want to praise or criticize that figure.
Make a list of the key points of your selected topic. Most of these points should be the things that you want to exaggerate in your poem.
Create a list of exaggerated images and/or similes to express your key points.
Decide on the poetic form that you want to use for your poem. You can choose any form, but for your poem to be the most effective you should use a form that suits your topic or feeling about that topic. Refer to the "Poets Garret" for a comprehensive list of poetic forms, a link to which is provided with this article.
Write an outline for your poem stanza by stanza or line by line if it is particularly short. In this outline, organize your key points and hyperbole images so that they fit the poetic form that you chose.
Write a draft of your poem based on your outline.
Edit your poem until you are satisfied with the results.