For resources to help take advantage of this period in the fullest possible way, see:
Orthodox Christmas Resource Page
The following sermons by St. Leo the Great were delivered during the Nativity Fast to prepare the faithful for Christmas and Theophany. These sermons were delivered during the "tenth-month," i.e. December. This coincides with our modern fast season of Advent. December still means "tenth-month," but is the actual twelfth month because of the addition of July and August, added later.
On the Fast of The Tenth Month, I
On the Fast of the Tenth Month, V
On the Fast of the Tenth Month, VI
On the Fast of the Ten Month, VIII
How did the contemporary Nativity Fast come to be?
The first mention of a preparatory period before Christmas is mentioned in a decree of the Synod of Saragossa (380). The Synodal Fathers stated that every Christian should daily go to church from December 17th until the Theophany (January 6th). At the Synod of Mac (581) in Gaul (present day France) it was decreed that from November 11th, the day of St. Martin, until December 24th every Christian should fast three times a week (Monday, Wednesday, Friday).
Our pre-Nativity period of preparation developed rather late. Scholars do not agree about the exact time it began. Some hold that it began in the sixth century. Others believe it began in the seventh or eighth century. The present liturgical pre-Nativity season was finally established at the Synod of Constantinople (1166). This Synod decreed that the fast would begin on November 15th and last until December 24th. Thus, there was created another forty day fast.
The pre-Nativity fast is often called "Philip's Fast" because it begins on the day after the feast of St. Philip the Apostle. The fast was introduced to prepare the Church for a worthy celebration of the great and holy day of the Birth of Christ, with our participation in the Divine Liturgy for that day. The regulations for the fast were far more lenient than the Great Fast of Lent before Pascha. Only Monday, Wednesday, and Friday were days of strict fasting without meat or dairy products (or oil in Slavic countries). On Sundays fish was permitted. Lay people were at first permitted to eat fish on other days, too, until the monastic rigoristic influence prevailed, which was considered beneficial for the entire Church and not just monastics.
It is interesting to observe that the famous 12th century Byzantine canonist Theodore Balsamon expressed the opinion that it would be enough if the lay people fasted only one week before Christmas. In 1958 a modern Greek author, Christos M. Enislides, welcomed Balsamon's suggestion and believed that the best solution would be for the Church at large to abstain from meat and dairy products for 33 days; during the last seven days of the fast everybody should observe the strict fast. But for now this is a mere proposition and should not be seen as the rule.