A pastiche poem is one that imitates the style of another famous poem. A pastiche imitates the style, form and sometimes the subject matter of the original poem just like a parody. However, unlike a parody, a pastiche is not written to mock or satirize the original poem. Instead, a pastiche is written as an homage. It is also an exercise that writers can use to hone their craft by learning about style and technique from another writer.
Study the Style
Before you can write a poem imitating another poem, you need to understand what makes the original distinct. To do this, you need to study the style of the poem. Determine if the poem falls into a particular literary style, such as Romanticism or Modernism. If so, this will determine the content of your pastiche. For example, Romantic poems emphasized subjectivity and feeling, and they used nature as a backdrop or symbol of expression. You would need to adhere to those same characteristics in your pastiche.
Determine the Form
While some poems are written in free verse, a great many more adhere to a particular form. You will need to determine the form of the poem that you want to imitate before you can write your pastiche. Some examples include sonnets, ballads, epics and elegies. When you write your pastiche, you will need to adhere to the characteristics of the form. For example, an English sonnet has three quatrains and ends with a rhyming couplet. The pattern for the rhymes in an English sonnet is abab cdcd efef gg. When writing a pastiche of an English sonnet, you would need to use this same rhyming pattern and form.
Choose Something to Change
Of course, you can't copy everything about a poem. That would be transcription, not writing. You will have to choose something to change about the poem to write your pastiche. Some possibilities include the setting, the characters, the plot, the point of view or the dialogue. Of course, if you change one of these elements, it can change other elements. For example, if you changed Annabel Lee to a dog named Cannibal Flea, that would probably change the whole plot of the famous poem by Edgar Allen Poe -- or maybe not. You can choose as many elements as you want to change. The key is to stick to the style, form and conventions of the poem.
Advance the Poem
The key to writing a pastiche is not just to imitate. The practice is supposed to help you learn more about your own writing and make it better. Therefore, you should also find a way to advance the poem. Maybe you create a contrast that reveals an irony about the characters, or you use a point of view that creates new understanding of the subject matter. You don't necessarily have to try to create a new masterpiece, but you should aim to create something new.