Rituals are conducted at the Altar, and are learnt through finding Tomes of Knowledge. When you find a Tome, it will give you an advancement. The Rituals you can cast are dependent on which advancements you have. All Rituals can be cast if you are in creative mode.
Rituals can have many effects, and a list of them can be found here.
Casting a Ritual
You cast Rituals through the Altar.
Rituals require a certain amount of Amethyst Flux to cast. You cannot start a Ritual if you have less than half the required amount of Amethyst Flux specified by the Ritual. If you run out of Amethyst Flux in your Altar midway through the Ritual, unexpected Bad Things will happen.