Question: "How are the 12 days of the Nativity Feast numbered? Does it start on the Feast itself or the next day? Is the last day of the feast the 12th Day?"
The twelve days of Christmas begin on the feast, and end on the eve of Theophany. The idea of zero as a number is not an ancient one, and so the feast itself is not day zero, but day one, of the twelve days.
In one sense, you could say Christmas is one day, the day of the feast. But then we especially celebrate the next two days, and so in another sense you could speak of three days of Christmas. But then the feast of Christmas actually is celebrated for 7 days, from December 25th through December 31st (which on the civil calendar falls on January 7th through January 13th). December 31st is the Apodosis of the feast (or the Leave-taking of the feast). In more ancient times, the Apodosis of Christmas was actually celebrated with the feast of the Circumcision of the Lord (January 1st o.s. / January 14th n.s.), but when the feast of St. Basil was combined with it, the Apodosis was moved up one day (Archbishop Job (Getcha), The Typikon Decoded, (Crestwood, NY: St. Vladimir Seminary Press, 2012), p 136). Beginning on January 2nd o.s. / January 15th n.s., we begin to celebrate the forefeast of Theophany. So the last of the 12 days of Christmas is the eve of Theophany (the last day of the forefeast).
In the priest's service book (sluzhebnik), it says in the menologion for December 25th:
"Three-day feast, and all [foods] allowed. Likewise, a twelve day dispensation for all [foods]...."But as with many Orthodox rubrics, there is always a "but..." We dispense with the fast for twelve days, but since the twelfth day is the eve of Theophany, we don't dispense with it entirely on that day -- it is a day on which wine and oil may be consumed, but otherwise a fast day.
In very ancient times, Theophany was actually the combined celebration of the the Nativity of Christ and His Baptism. The practice of celebrating the Nativity on December 25th developed in the western part of the Church, and then spread to the east. And so, Theophany and Christmas are closely linked, and in a certain cense, Theophany is a continuation of the Feast of the Nativity, and we celebrate Theophany for eight days. I have seen Russian Christmas stars that have an icon of the Nativity on one side, and an Icon of Theophany on the other. And so on your Christmas tree, you would simply flip the star on the feast of the Theophany.
However, in another sense, you could even say we celebrate Christmas for 40 days, because on the 40th day, we mark the feast of the Meeting of the Lord (February 2nd o.s. / February 15th n.s.) -- on which day Christ was brought into the temple, and met by St. Symeon and the Prophetess Anna.
So, as is often the case with the Orthodox Faith, there are more than one answers to the question that are all correct, but none of which tell the whole story exhaustively.
For More Information:
Stump the Priest: The Nativity Fast and Christmas Parties
Stump the Priest: Is Christmas Pagan?
Stump the Priest: Fasting on the Eves of the Nativity and Theophany
Why the Russian Orthodox Church Celebrates Christmas on January 7th
Wikipedia: Twelfth Night (Holiday)
