Morgaine believed in an ancient Celtic/ Druidic religion. It involved worship of Ceridwen, the Mother Goddess. The highest holiness was to give yourself over to the flow of nature. So, it was kind of a nature religion. The head of Morgaine's religion was the Lady of the Lake, the high priestess, and her male counterpart, the highest ranked Druid, called the Merlin. Women were considered more important than men, for instance, the Lady was above the Merlin, and geneology was always traced through the women. Avalon was the sacred island where the Lady and the priestesses and druids lived.

The rituals in Morgaine's religion were for blessing the land during harvest, festivals, or kingmaking. They sometimes involved fasting or taking a vow of silence or abstinence- such things were thought to build up magic power for the festivals. They also took special herbs to induce the Sight (a prophetic trance state) or did sacrifices.

I wanted to add, I do not believe in this stuff! I am a Christian, and only included this so people could understand the book more fully. MZB herself said that she had partially invented this religion to best suit the needs of fiction.

Here's something MZB's secretary sent me about the religious beliefs:
She [MZB] is a Christian herself, and the negative things the Christians say in MISTS are generally accurate quotes of some of the more mysogynistic early Church Fathers. The book is not intended to be anti-Christian; it's an attempt to tell the story from the losing side.