Alexander grew up in Pennsylvania during the Great Depression. He developed a passion for reading books and writing poetry. He attended college for only one term, believing that there was nothing more college could teach him. He enlisted in the United States Army and rose to be a staff sergeant in intelligence and counter-intelligence. He met his wife while he was stationed in France and studied French literature at the University of Paris. After returning to the United States with his new family, he struggled to make a living from writing until he published "And Let the Credit Go" (1955), his first autobiographical novel. His interest in Welsh mythology led to the publication of his series "The Chronicles of Prydain".