Some of the most popular and interesting myths of a culture are the origin myths.
1) Look up a myth and pick a subject within the myth--a human, an animal, a deity, etc--and describe its origins. 
2) Describe the origin of the myth itself, simply as a story. How do these stories develop and expand? What makes a myth? What is the relationship between mythology, faith, and fiction?
Trace each thread of your subject to its possible beginnings. Determine what makes a myth and what it reflects about the people who believe it.