Saints Athanasius and Cyril, both bishops of Alexandria and Doctors of the Church, are the doctors most closely associated with the dogma declaring Mary to be the Mother of God. Here is an example of Athanasius' writings; note that it is the second reading in today's Office of Readings in the Liturgy of the Hours. The Council of Ephesus, at which Cyril presided, formalized the dogma. It is important to realize how a correct understanding of Mary as Mother of God is critical to understanding the Personhood of Jesus Christ Himself.
So today all faithful Catholics participated at Mass since this solemnity is a Holy Day of Obligation. Traditionally on this day the recitation of the Veni Creator is attached to a plenary indulgence (other conditions applying of course). There are a few other key things about today.