Choose a moral. This is the most crucial step, as fables exist to teach morals. No matter how good your characters and rhymes are, they are useless without a solid moral. The moral should be clear, definite, and uncontroversial. "Hard work pays off" and "Tell the truth" are examples of solid morals.
Find a situation. Now that you have your moral, think of how you can most effectively teach it. Although they don't have to, since fables usually involve animals, try to think of a situation in the animal kingdom that teaches your moral, for instance how "The Ants and the Grasshoppers" teaches not to be lazy. Again, the key is simplicity. Fables are not complicated or nuanced, so you should have no more characters or situations than absolutely necessary.
Select a rhyme scheme for your poem. A short simple story should have a simple rhyme scheme such as ABAB, AABB, ABBA or ABAC, where "A" represents one pair of rhyming words and "B" another.
Write the fable. This is tricky since you must effectively tell the story and follow your rhyme scheme, but the end result will be an educational poem that's fun and might be cherished for generations to come.