Unlike the Birthright Ceremony, the Offering to the Darkness is a personal journey into the darkness. There is no big gathering or event and there is no Priestess to oversee the ceremony, though they are often done at an altar where a Priestess can give them guidance in what is to follow. Personal family may come to stand watch over the altar where the offering is being given, but that is about it.
The Offering Ceremony always lasts from sunset to sunrise as that is the best time to commune with the Darkness. During this ceremony, you will be granted with your Offering Jewel, which can be up to three ranks darker. For example, if you were given a Tiger Eye Birthright, you can walk away from Offering to the Darkness with a Rose Jewel, a Summer-sky Jewel, or a Purple Dusk Jewel. There is a tiny possibility of not receiving an Offering Jewel though.
If you did not receive a Birthright Jewel, you can still receive an Offering Jewel, though you are restricted to only a single or a semi-descent at that point. What this means is you can either receive a White Offering Jewel or a Yellow Offering Jewel after your Offering to the Darkness is performed, but no darker than that.