Research epitaph poems to get a feel for how epitaphs are written. Famous epitaphs can be found on websites such as Famous Quotes at famousquotes.me.uk, or by visiting a local cemetery and looking at the epitaphs written on the tombstones there. Epitaph poems often follow common literary forms and verses, so find literary resources such as the Bible or various poetry books to learn about the lyrical quality of poems.
Write down descriptions of the person's life and personality. You may not remember everything about the person all at once, so it can help to keep a journal and write down what you remember throughout the day. This could be anything from that person's personal philosophy; their history; funny, tragic or poignant moments; or things that she said.
Write down the important roles the person played in life. This person could have been a parent, a grandfather, an artist, or military personnel. Even if the person won no special awards or wasn't known on a large scale, there are still relatives and friends who this person impacted and influenced throughout her life.
Decide what qualities or accomplishments you want to focus on. If you're having difficulty deciding, take the journal or whatever writing you have, and then write down several qualities or accomplishments on a piece of paper. Take time to narrow down the qualities or accomplishments throughout the day until you have decided a focus for the deceased's epitaph poem.
Create the poem. Write the poem in a calm state of mind, when you have time to relax and be alone. It might help to light some candles, play soothing music, or burn incense. Typically epitaph poems are short and memorable, as they have to be small enough to fit onto a gravestone. The epitaph poem does not have to rhyme, but it should be lyrical and flow smoothly. Keep the notes about the deceased close at hand for reference.
Put the epitaph poem away for a day and then later take the poem out to edit it. Read the poem out loud to check for consistency and smoothness. Reword lines and words that seem clunky or out of place. Ask relatives or trusted friends for advice on how to improve the poem. Make the necessary changes.