The Liturgy of the Hours is known as the universal prayer of the church. Priests and clergy are obligated to say the Office every day. It is essentially one of the higher forms of prayer, and is a wonderful practice for the laity to pray it daily, even if you can only squeeze in one or two of the hours each day. For priests, the obligation includes reciting the Office of Readings, Lauds, or Morning Prayer, one of the daytime hours (Midmorning, afternoon, or midafternoon,) Vespers, or Evening Prayer, and Compline, or Night Prayer. Traditionally, the Office of Readings is recited as the first hour of the day, and immediately precedes Lauds, however, the Office of Readings can be said at any time of the day. Lauds is usually said at first morning's light, or as soon as you wake up. This can be as early as 5AM, or as late as about 8AM, but of course, for laity, the time at which the hour is recited isn't quite as important. The daytime hours are fairly flexible too, but each hour gives you a good idea of when it should be recited (midmorning, afternoon, or midafternoon). Vespers is usually recited as the day draws to a close, but when it is still somewhat light out. (5PM-7PM or so). Again, all the times mentioned here are simply suggestions, not requirements. (At least for the laity.) Compline is usually recited after nightfall has come, but many people say it immediately before going to bed. I prefer to say it about thirty minutes before retiring, because if I recite it immediately before bed, I am usually very tired, and tend to rush a little.
The Office of Readings contains a hymn, three Psalms and an antiphon for each, a reading from the Bible, and a reading from the early church, such as an excerpt from an ancient homily, or writings of the Church fathers. This hour will take approximately 15 minutes to say, but can be shorter or longer, depending on the day
Lauds, or Morning Prayer consists of a hymn, three Psalms and an antiphon for each, a short reading, a responsory, Canticle of Zechariah with antiphon, intercessions, and a closing prayer. This hour takes about 10 minutes to say, but can be shorter or longer, depending on the day
The daytime hours each consist of a hymn, three psalms, a reading, a brief verse, and a closing prayer. Any one of these hours takes about 7-8 minutes to say.
Vespers, or Evening Prayer consists of a hymn, three Psalms and an antiphon for each, a short reading, responsory, Canticle of Mary (Magnificat) intercessions, and a closing prayer.
Compline, or Night Prayer, consists of a hymn, examination of conscience and penitential rite, one psalm, a brief reading, responsory, short Gospel Canticle, and a closing prayer. This hour takes around 5 minutes to say, but may be shorter or longer, especially if you add more than one verse of the hymn. At the end of Compline, a hymn to the Blessed Virgin is sung or recited, and can be as simple as saying the Hail Mary. I personally sing the Salve Regina.
Again, please note, the length of these hours is only a rough approximation, and the length of time it takes to recite each hour can vary greatly.
Before the first hour that you recite each day, no matter what that hour may be, the Invitatory Psalm should be recited before it. This Psalm can be found in the Ordinary of your Breviary. The Ordinary comes immediately after the Proper of Seasons, which, in the four volume set, is the first section. In the Christian Prayer, the Ordinary begins on page 686. The Invitatory consists of one of several Psalms and an antiphon. The Psalm that is used most often is Psalm 95. The antiphon is recited after each strophe, or section. All Psalms in the breviary are separated into strophes, and can be differentiated by looking for the spaces in the Psalms. This antiphon will be found in the Ordinary as well, and varies depending upon the liturgical season. For feast days and solemnities, this antiphon will be found in the Proper of Saints, which is usually found immediately after the Psalter, and begins on page 1060 of the Christian Prayer breviary.
For all Psalms, at the end of each, the Glory to the Father is recited, usually while bowing. However, the wording is traditionally changed slightly to: "Glory to the Father, and to the Son, and to the Holy Spirit, as it was in the beginning is now and will be forever, Amen." However, if you want to use whatever version of the Glory to the Father you are familiar with, you absolutely can do that.
The antiphon for the Psalms will always be found in the Psalter, and it is recited immediately before each Psalm, and then after the Glory to the Father at the end of each psalm. This goes for all the hours.
Each hour is preceded by saying: "God, Come to my assistance, Lord make haste to help me," and then the Glory to the Father. As you are saying "God, Come to my assistance," you should make the Sign of the Cross.
Morning Prayer and Evening Prayer are closed by saying: "May the Lord bless us, protect us from all evil, and bring us to everlasting life, Amen" Once again, you should make the Sign of the Cross as you say this. Night Prayer is closed by saying "And may the all-powerful Lord grant us a restful night, and a peaceful death, Amen" Again, the Sign of the Cross is made at this time.
The Proper of Saints contains texts for feast days. Some feast days do not have special psalms and antiphons, and some only have a different antiphon for the Canticle of Zechariah and the Canticle of Mary.
On Sundays and Solemnities, there are two Evening Prayers. First is Evening Prayer I, and then Evening Prayer II. Evening Prayer I for a Sunday is said on Saturday night. For a solemnity, Evening Prayer I would be said the evening before the solemnity. Evening Prayer II, obviously, is said on either Sunday evening, for a Sunday, or the evening of the solemnity. Please remember, that a solemnity is not the same as a feast day. A solemnity is a much more solemn event in the Church. A feast day has no Evening Prayer I and Evening Prayer II. A solemnity does have Evening Prayer I and Evening Prayer II.