Write down you thoughts and memories of the person you are commemorating. Include some specific events and images from your time with that person.
Organize your elegy poem into stanzas. Most poems have the same number of lines in each stanza. For example, you can have a poem that consists of 16 lines, which you separate into four stanzas with four lines each. Make sure you have an even number of lines in each stanza.
Pair your lines into rhyming couplets--two lines each. Because you have an even number of lines in each stanza, you should be able to group the lines together easily. While not all elegies rhyme, many famous elegies do rely on rhyme to establish the rhythm of the poem, such is the case with the famous "O Captain! My Captain!" by Walt Whitman.
Conclude the poem with final remarks that leave the audience with a question, conclusion or implication. For example, in "A Refusal to Mourn the Death, by Fire, of a Child in London", Dylan Thomas ends the poem with the uplifting idea that there is no more death after a person's initial death. This type of thought-provoking punch line at the end of a poem can provide good closure for your audience.
Title your elegy. It is often advised that you come up with the title after you finish writing your elegy, so that your title befits the ideas that surface in your poetry. Once you've come up with a title, place it at the top of the page.