How to Write a Modern-Day Greek Myth
Think of a natural occurrence that is not easily understood without modern science. The Greeks used myths to explain the world around them, with the Gods often causing such phenomena as the seasons and storms. To write a Greek myth, you could also choose something that happens in the natural world, the cause of which is not immediately obvious. Volcanoes and earthquakes are some examples.
Create characters. In Greek mythology, the protagonists were often heroes or Gods. The Gods tended to have special powers; for instance, Zeus could transform himself into other forms, such as animals, and was said to be behind the rain and drought.
Meanwhile, the heroes were also remarkable. Heracles, for example, was a demi-God -- his father was Zeus but his mother was a mortal -- and he successfully completed many feats, including ridding the city of Troy of a monster.
Bear such characters in mind when deciding who shall be the protoganists in your story. Remember that their special powers should be used to cause the natural occurrence you chose. If you are writing about a volcano, you may want to create a character that lives beneath the ground and punches the world above when he's angry, causing an explosion on the surface of the Earth.
Imagine an initiating incident. An initiating incident is the event that sets the ball rolling in a story. In Greek mythology, the Gods often punished mortals for doing wrong. It may be that the mortals in your story have indulged in unacceptable or immoral behaviour and the natural occurrence is doled out as a consequence.
Write about conflict. The middle section of stories often explores conflict between characters, which is resolved at the end of the tale. Greek mythology was often based around dualities, such as the fight between good and evil or light and dark. Take the conflict that has arisen from the initiating incident, which may be the mortals being punished for wrong doing, and attempt to resolve it. This could take the form of the mortals attempting to appease the gods, for example.
Write an ending that resolves the issue and teaches the reader about life. Greek myths often attempted to answer questions such as "Why are we here?" and "What is our purpose?" as well as conveying the proper way to live and values by which to live.