100. Pastors of souls should see to it that the chief hours, especially Vespers, are celebrated in common in church on Sundays and the more solemn feasts. And the laity, too, are encouraged to recite the divine office, either with the priests, or among themselves, or even individually.I would really recommend becoming familiar with this, the Church's prayer. When you pray the office, whether alone or in common, you are joining with thousands and thousands of Christians around the world in the act of sanctifying time. I especially like to think of the cloistered monks and nuns whose primary business it is to do this "work of God," (opus dei) to use the Benedictine word for it. They get the privilege of chanting the whole things. There are resources that would allow even the lay person at home to chant at least some of it.
The liturgy of the hours is by far my most favorite way to pray. I try to pray at least one office (usually Morning Prayer) every day. The psalms, as you can tell by some of my previous posts (e.g. here and here), are for me the true meaning of Christian prayer.
The complexity of the liturgy of the hours can seem a little daunting at first, but read carefully, be patient, and ask for help. Also, I get tired of prayer Ps. 63, the Canticle of the Three Young Men, and Ps.149 so often (Sunday of Week I, every feast and solemnity), but then again we pray the Benedictus and the Magnificat (and the Nunc Dimittis) every day, and I don't get tired of them.
By far the most popular version of the Liturgy of the Hours is the one published by Catholic Book Publishing Company, featuring the entire text for Morning and Evening Prayer, the daytime and night office, and (minimal) selections from the office of readings, plus selected hymns and chants. The Grail version of the psalms used in this and other editions is very good (Oh, I'm sure you could find things to nitpick about: Go ahead, that is what the comments box is for).
There are also other editions by other publishers. And, there is a shorter version that includes only the four week psalter for morning and evening prayer (I have one of these as well). And, if you really have a lot of time to pray, you can get the complete four-volume set with all of the office of readings in it. I was fortunate to inherit a complete Latin edition, which is what I use to pray.
Classically, and according to the rule of St. Benedict, all 150 psalms were recited in a week, pretty much in order. Now they have been arranged in a four-week psalter ("So that it may really be possible in practice to observe the course of the hours proposed in Art. 89, the psalms are no longer to be distributed throughout one week, but through some longer period of time." SC 91) Although the psalms are still very roughly in order, there is an attempt to be somewhat thematic, by putting evening songs in the evening, morning psalms in the morning, and psalms like 118 on Sunday. Some monastic communities, such as the Christ in the Desert and the Cistercians in Sparta, WI, still use the old 150 psalm/week psalter, I presume with permission.