Well, I don't think you need a belief in the supernatural to have a religion, the Buddhists have shown us that. In dealing with beliefs and theology, it's important to note that UUism is a way of being religious rather than a religious doctrine. For us, religion is an ongoing search for meaning, purpose, value and spiritual depth in one's life.
Well I described our Sunday services earlier so I guess you're asking about special days/holidays?
Birth, marriage, death - we mark all of these occasions with ceremony. These ceremonies are not considered sacraments. The minister tailors each service to the people personally involved, so that the ceremony will be especially appropriate to them.
The type of ceremony varies by congregation; there is no officially sanctioned induction ceremony. Two or three times each year, many congregations conduct an informal ceremony as part of a Sunday service in which new members are formally welcomed to the church.
We celebrate holidays such as Christmas and Easter. The difference may be that we tie these holidays more to the changing seasons than we do to traditional Christian themes. They are honored as celebrations of the winter solstice and the spring equinox -- the hope and promise symbolized by the lengthening of the daylight hours in December, and the renewal of life in spring after the winter season of darkness.
The traditional accounts of the birth of Jesus and of the Resurrection are sometimes included in these celebrations and cited as myths which contain a positive message about human life. The birth of a child, for example, represents the hope and promise found in each new life. The crucifixion and Resurrection are symbolic of how new life can emerge even after a time of pain and suffering. As with the Bible itself, these stories are not taken literally but for what they symbolically tell us about human life.
We celebrate Easter as the return of spring and the renewal of life; in this respect we draw more on the pagan rather than the Christian origin of this holiday. The New Testament accounts of the Resurrection may be cited as a symbol of the strength, power and renewal of life. We do not accept the idea of a physical resurrection.
Also, it varies from congregation to congregation, but will we celebrate and recognize holidays and holy days of other religions as well. Though practices vary in our congregations and change over time, UUs celebrate many of the great religious holidays. Whether we gather to celebrate Christmas, Passover, or the Hindu holiday Divali, we do so in a universal context, recognizing and honoring religious observances and festivals as innate and needful in all human cultures.