Write an outline of the letter that you want to write, including all of the major points that you want to touch on in your letter. For example, if you are writing about a recent vacation, your major points might be where you went, the sights that you saw and the impressions that these sights made on you.
Write out a list of images, similes, metaphors or other poetic devices that you want to use in your poem. Create these poetic devices with your major points in mind so that each main point pairs with one poetic device. Continuing with the example of the vacation, if you went to Seoul during the summer (one major point) and were impressed with how busy but laid back the people were (another major point) you could write that "the air was dragon's breath" (a metaphor, one poetic device) and that the locals "leaped around like dolphins on a mission" (a simile, another poetic device). For a list of poetic devices to consider, see the link to the Undergraduate Writing Center at the University of Texas at Austin in the Resources section.
Decide on the details of poetic form that you want your letter to follow. The epistle form itself has no strict rules, so your epistle's meter, rhyme scheme and division into stanzas are entirely up to you. As an example, you could choose to write in three-line stanzas with the first and last line rhyming (ABA pattern) and decide to make each line 10 syllables long (perhaps in iambic pentameter).
Write a draft of your epistle from your list of key points and your list of poetic devices. If one of your key points was visiting Seoul and you described it as "the city of a thousand lights and a million people" and another key point was the busy, but relaxed attitude of the people there which you described as "leaping dolphins," then you could write something like this:
"Visited Seoul, that city of thousands
Of lights, of millions of people. Bustling
Through streets like loyal leaping dolphins."
Change words as necessary to create alliteration as you see fit. Use your thesaurus as a means to find replacement words. For example, if you started with this line:
"Visited Seoul, that city of thousands"
To bring another "s" alliterative word into this line, you could look up "Visit" in your thesaurus and change it to "Saw." Your revised first line, then, would look like this:
"I saw Seoul, that city of thousands"
Edit your alliterative poem letter until you are satisfied with the results.