Choose a topic, theme or story to write about. The topic should be one you know well or can imagine many details about. It may help to write out a description ahead of time so that you know what you want to say. Brainstorm as many details as you can, but do not expect to use them all.
Decide whether your quatrains will rhyme or not. If they will be rhyme, select the rhyme scheme you would like to use. A common rhyme scheme is abab, in which every other line rhymes. For example:
The war was long; we joined the FIGHT
We fought through night and DAY
with enemies on left and RIGHT
we slowly made our WAY.
Another possible rhyme scheme is abcb, in which only the second and fourth lines rhyme. For example:
I've planted all my garden seeds--
my roses, peas, TOMATOES.
I don't know when they'll all come up
but I'm hungry for POTATOES.
Make a list of possible rhymes you will use. Try using two-syllable words or words that don't rhyme exactly. These will make your poem more surprising and interesting. For instance, "love" and "dove" is a conventional and expected exact rhyme. "Love" and "stove" is an inexact rhyme where the two words have an interesting relationship to each other -- the idea of domestic life. There are many rhyming dictionaries that can help you find rhymes. Your list will provide you with numerous options as you write.
Choose an existing ballad or hymn if you want to try writing in a regular rhythm or meter. Meter means that the poem has a regular pattern of stressed and unstressed syllables. You can often hear the meter as "ba-DUM ba-DUM ba-DUM ba-DUM." One famous ballad written in meter is "The Yellow Rose of Texas."
the YELLow ROSE of TEXas
the FAIRest SIGHT to SEE
no OTHer LOVer KNOWS her
no OTHer ONE but ME
If you sing the song out loud, you will be able to hear the meter better. Choose a poem you like if you want to try imitating its rhythm. Don't be afraid to allow the rhythm to vary a little from the original. It does not need to be exactly the same to be good.
Read your poem out loud once you are finished, and listen for places where you could make it sound better. For example, you may wish to change to a more descriptive word ("mud" instead of "ground" if you want the idea of something gooey, wet and cold). You may also want to play with more interesting or different rhymes. For example, instead of "might" and "right" as a pair of rhymed words, you may decide to try "in flight" and "eyesight." Take your time. Quatrain poems can be difficult at first, but they are fun to write and get easier the more you practice.