The daily cycle of Morning Prayer and Evening Prayer is called The Daily Office. The texts for both offices are outlined near the beginning of the Book of Common Prayer. However, not every part of the sequence in the Prayer Book is carried out at Saint Thomas, in large part because Morning Prayer and Evening Prayer are followed by a Mass. So, for example, since we say the Lord's Prayer in the Mass, we don't also say it as part of Morning Prayer. Similarly, since we say the creed in Morning Prayer, we don't say it again in the Mass that follows.
As Saint Thomas, we follow this sequence for Morning Prayer: (1) opening sentence and responses, (2) the Venite, (3) one or more psalms appointed for the day, (4) the lesson appointed for the day, (5) the Benedictus, (6) the Apostles' Creed, (7) more responses, (8) a Collect for Peace and a Collect for Grace, and (9) the grace (1 Cor. 13:14).
Because it is abbreviated, Morning Prayer generally only lasts about ten or twelve minutes. The Mass that follows usually lasts about twenty minutes. So combined, they will take about a half hour or a bit more of your time. If you choose to attend, it just might be the best half hour of your day.
If you look at the lessons assigned for Morning Prayer each day, you'll notice they are in sequence. The Daily Office lectionary breaks the Bible down into lessons to be read daily in a two-year cycle. Therefore, if you attended every service of Morning Prayer and Evening Prayer at Saint Thomas for two consecutive years, and also attended all the Masses that followed, you would be exposed to a large portion of Holy Scripture. If you repeated the cycle five times, you'd have a biblical mind in a decade's time. And the Word of the Lord would be an old and trusted friend.