Part of praying the Hours, or really any Prayer Rule, is the Psalter. In the Roman Catholic Liturgy of the Hours, you pray most of the Psalter over a four-week cycle. In the Eastern Churches, the Psalter is divided into twenty sections or parts, called Kathisma, and you pray the entire thing once a week. (Twice weekly during the Great Fast).
This is my first Philip's Fast as an official Ruthenian Byzantine Catholic, so I am trying to incorporate some Eastern practices into this period of preparation for the Nativity of Our Lord God and Savior Jesus Christ. Silvia, who blogs here, is doing a Kathisma Psalter prayer group in which participants each pray one Kathisma each day for the period of the Philip's Fast, praying the Psalter twice through in that time. You are assigned a beginning Kathisma and then you just pray them in order every day - this means that every day the entire Psalter is prayed, and because the names are on the post I linked, we are all praying for each other. I think that's beautiful!
As for the rest of what I'm doing for the Fast, I am of course adhering to the St. Martin's Fast guidelines of the Confraternity of Penitents and will try to be vegan on Wednesdays and Fridays (too much vegan makes me cranky, I have to have a bit of cheese or some cream in my coffee). This, plus the rotating Psalter prayers, the Hours and my other intercessory prayers, should make for a (hopefully) fruitful Philip's Fast.