Smith was born in China to Methodist missionaries and spent his first 17 years there. Upon coming to the United States for education, he studied at Central Methodist University and the University of Chicago.
During his career, Smith not only studied but also practiced Vedanta (studying under Swami Satprakashananda, founder of the St. Louis Vedanta Center), Zen Buddhism (studying under Goto Zuigan), and Sufism of Islam for more than ten years each.
As a young man, Smith suddenly turned from traditional Methodist Christianity to mysticism, influenced by the writings of Gerald Heard and Aldous Huxley. In 1947, before moving from Denver to St. Louis, Smith set out to meet with then-famous author Gerald Heard. Heard responded to Smith's letter, inviting him to his Trabuco College (later donated as the Ramakrishna Monastery) in Trabuco Canyon, Southern California. Heard made arrangements to have Smith meet the legendary author Aldous Huxley. Smith recounts in the 2010 documentary Huxley on Huxley meeting Huxley at his desert home. Smith was told to look up Swami Satprakashananda of the Vedanta Society once he settled in St. Louis. So began Smith's experimentation with meditation and association with the Vedanta Society of the Ramakrishna order. Smith developed an interest in the Traditionalist School formulated by René Guénon and Ananda Coomaraswamy. This interest has become a continuing thread in all his writings.
Due to his connection with Heard and Huxley, Smith went on to meet Timothy Leary, Richard Alpert (Ram Dass), and others at the Center for Personality Research, where Leary was research professor. The group began experimenting with psychedelics and what Smith later called "empirical metaphysics". The experience and history of the group are described in Smith's book Cleansing the Doors of Perception. During this period, Smith was also part of the Harvard Project, an attempt to raise spiritual awareness through entheogenic plants. During his tenure at Syracuse University, he was informed by leaders of the Onondaga tribe about the Native American religious traditions and practices, which resulted in an additional chapter in his book on the world's religions. In 1990 the Supreme Court ruled that the use of peyote as a religious sacrament by Native Americans was not protected under the US Constitution. Smith took up the cause as a noted religion scholar. With his help in 1994, Congress passed the American Indian Religious Freedom Act amendment, providing legislative protection to a religious practice that the Supreme Court had decided lacks constitutional protection.