What is  Liturgy of the Hour?

"Seven times a day I will praise you" - Psalm 118 (119): 164

God has commanded us to pray without ceasing, and this is what the Hour helps us to do.

Morning Prayer - at the beginning of day work and the arrival of light.

Daytime Prayer - in the middle of the morning, noon and evening, to unite us with who we are and through whom we work.

Evening Prayer - at the end of the working day, to offer what we have done.

Night Prayer - the last thing in the night, to praise our souls to God.

And finally, there is the impressive Reading of the Office, at any time best for us to contemplate the mysteries of  salvation, with the help of the Scriptures and the writings of the Church Fathers.

"The purpose of the Divine Office Reading is to sanctify the day and all human activities." - Apostolic Constitution, 

The Liturgy of the Hour is the single strongest source of prayer of the Christian Church, with prayers, psalms and readings for each Hour, changing daily and through the seasons

"The office ... prayers not only from the priest but for all God's people." - Apostolic Constitution, Canticum Laudis.

Current Roman Catholic usage focuses on three major hours and from two to four minor hours:

The Office of Readings or the Officium lectionis (formerly Matins), major hour

Morning Prayer or Lauds, major hour

Daytime Prayer, which can be one or all of:

* Midmorning Prayer or Terce

* Midday Prayer or Sext

* Midafternoon Prayer or None

Evening Prayer or Vespers, major hour

Night Prayer or Compline

All hours, including the minor hours start with the verse Ps 69/70 v.2:

God, come to my assistance.

— Lord, make haste to help me.

Followed by the doxology:

Glory to the Father, and to the Son, and to the Holy Spirit:

— as it was in the beginning, is now, and will be for ever. Amen. Alleluia.

The verse is omitted if the hour (either Morning Prayer or Office of Reading) begins with the Invitatory.

The Invitatory is the introduction to the first hour said on the current day, whether it be the Office of Readings or Morning 

The opening is followed by a hymn. The hymn is followed by psalmody. The psalmody is followed by a scripture reading. The reading is called a chapter (capitula) if it is short, or a lesson (lectio) if it is long. The reading is followed by a versicle. The hour is closed by an oration followed by a concluding versicle. Other components are included depending on the exact type of hour being celebrated.

In each office, the psalms and canticle are framed by antiphons, and each concludes with the traditional Catholic doxology.

Major hours

The major hours consist of the Office of Readings, Morning Prayer (or Lauds) and Evening Prayer (or Vespers).

The Office of Readings consists of:

opening versicle or invitatory

a hymn

one or two long psalms divided into three parts

a long passage from scripture, usually arranged so that in any one week, all the readings come from the same text

a long hagiographical passage, such as an account of a saint’s martyrdom, or a theological treatise commenting on some aspect of the scriptural reading, or a passage from the documents of the Second Vatican Council

On nights preceding Sundays and feast days, the office may be expanded to a vigil by inserting three Old Testament canticles and a reading from the gospels

the hymn Te Deum (On Sundays outside Lent, on days within the octaves of Easter and Christmas, and on solemnities and feasts)

the concluding prayer

a short concluding verse (especially when prayed in groups)

The character of Morning Prayer is that of praise; of Evening Prayer, that of thanksgiving. Both follow a similar format:

opening versicle or (for morning prayer) the invitatory

a hymn, composed by the Church

two psalms, or parts of psalms with a scriptural canticle. At Morning Prayer, this consists of a psalm of praise, a canticle from the Old Testament, followed by another psalm. At Evenning Prayer this consists of two psalms, or one psalm divided into two parts, and a scriptural canticle taken from the New Testament.

a short passage from scripture

a responsory, typically a verse of scripture, but sometimes liturgical poetry

a canticle taken from the Gospel of Luke: the Canticle of Zechariah (Benedictus) for morning prayer, and the Canticle of Mary 

(Magnificat) for evening prayer

intercessions, composed by the Church

the Lord’s Prayer

the concluding prayer, composed by the Church

a blessing given by the priest or deacon leading Morning or Evening Prayer, or in the absence of clergy and in individual  recitation, a short concluding versicle.

An Invitatory precedes the canonical hours of the day beginning with the versicle:

Lord, open my lips.

—And my mouth will proclaim your praise (Ps 50/51 v.17), and continuing with an antiphon and the Invitatory Psalm, usually 

All psalms and canticles are accompanied by antiphons.

Unless the Invitatory is used, each Hour begins with the versicle:

God, come to my assistance.

— Lord, make haste to help me. (Ps 69/70 v.2), followed by a hymn. Each Hour concludes with a prayer followed by a short 

versicle and response.

Matins or the Office of Readings is the longest hour. Before Pope St. Pius X’s reform, it involved the recitation of 18 

psalms on Sundays and 12 on ferial days. Pope Pius X reduced this to 9 psalms or portions of psalms, still arranged in three “nocturns”, each set of three psalms followed by three short readings, usually three consecutive sections from the same text. 

Pope Paul VI’s reform reduced the number of psalms or portions of psalms to three, and the readings to two, but lengthened these. On feast days the Te Deum is sung or recited before the concluding prayer.

After St. Pius X’s reform, the Office of Readings was reduced to four psalms or portions of psalms and an Old Testament canticle, putting an end to the custom of adding the last three psalms of the Psalter (148-150) at the end of Lauds every day. The number of psalms or portions of psalms is now reduced to two, together with one Old Testament canticle chosen from a wider range than before. After these there is a short reading and response and the singing or recitation of the Benedictus.

The Evening Prayer has a very similar structure, differing in that Pius X assigned to it five psalms (now reduced to 2 psalms and a New Testament canticle) and the Magnificat took the place of the Benedictus. On some days in Pius X’s arrangement, but now always, there follow Preces or intercessions. In the present arrangement, the Lord’s Prayer is also recited before the concluding prayer.

Midmorning, Midday and Midafternoon Prayers have an identical structure, each with three psalms or portions of psalms. These are followed by a short reading from Scripture, once referred to as a “little chapter” (capitulum), and by a versicle and response. The Lesser Litany (Kyrie and the Lord’s Prayer) of Pius X’s arrangement have now been omitted.

Prime (which is now suppressed and gone) and Night Prayer (Compline) also were of similar structure, though different from Midmorning, Midday and Midafternoon (Terce, Sext and None).

source -https://divineoffice.org/liturgy-of-the-hours/how-to-pray-the-liturgy-of-the-hours/