Liturgy of the Hours

Liturgy of the Hours is the Church's prayer. It fufills Paul's exhortation that we pray continually.
The prayers of the liturgy are available in several forms. On line there is Universalis and Liturgy of the Hours Apostolate. The former is free, but lacks all of the Antiphons, while the latter is a paid subscription service. There is a multi-volume set, costing ~ US$150 and a single volume, Christian Prayer, which contains the office. Each diocese in the United States, at least, also publishes a booklet listing all of the readings for each day of the specific year.
Using one of the online services is easy. the proper set of readings for each day is delivered to your computer, or mobile device. Using the single volume Christian Prayer can be quite challenging.
The full set of hours number seven. They are:

1. Matins, also called the Office of Readings
2. Lauds or Dawn Prayer
3. Terce or Mid-Morning Prayer
4. Sext or Mid-Day Prayer
5. None or Mid-Afternoon Prayer
6. Vespers or Evening Prayer
7. Compline or Night Prayer

The Christian Prayer book doesn't really have full set of readings. It is sufficient to pray Lauds, Vespers and Compline. Only one of the three day readings (Terce, Sext or None) is obligatory, and so only one set of day readings is included. An abreviated set of Office readings is included.
My copy of Christian Prayer has five ribbons to help mark readings. The book itself is divided into a section of Seasonal readings, a four week cycle of Morning and Evening Prayer, a Night Prayer section, a two week cycle of Day Prayer, a section of readings based upon the Calendar called the Office of Saints, a section of Common readings and an Ordinary, which contains rubics for Morning and Evening prayer.
So how do you use this somewhat complicated volume to actually pray the hours?
Start by deciding how much of the Office you're going to pray. Since I'm neither a priest nor a lay member of a specific order I typically only say Lauds, Vespers and Compline. The first step is to decide where on the Liturgical calendar today falls. If the day is during Lent, Advent or the Easter season then the readings will be found in the Proper of Season section of readings. If the day is a feast day or a solemnity then readings will be found in the Proper of Saints section, which is arranged by day and month.
So say today is Monday May 1st, which is dedicated to Mary. So go to the Office of Saints section and you'll find readings for Morning and Evening prayer (as well as the Evening Vigil i.e. the day before, because it is a major feast day.) If this is your first reading of the day start with the Invitatory. There will be an antiphon, which is in the Proper of Saints section followed by Paslm 100, which you'll find in the Ordinary.
After the Invitatory there will be a doxology. Glory be to the Father Son and Holy Spirit, As it was in the beginning, is now and ever shall be . Amen This is also said after each Psalm or Cantical.
Then there are three Psalms readings. Before and after each Psalm reading there is an antiphon. The antiphons come from the Proper of Saints or from the Common readings. This section has readings for Pastors, Doctors of the Church, Apostels, Holy Men, Holy Women, Martyrs, and Marian Feasts. So start in the Proper of Saints and it will direct you to the Common readings for Mary. The Psalm readings come from the four week cycles of Psalms. On a Feast day these Psalms are typically from Sunday of Week 1.
After the Psalms there is a Reading, typically from one of the Epistles. Then a Responsorial verse. The Benedictus, from the Ordinary. Intercessions. The Lords Prayer. The closing, from the Ordinary.
If the day is a memorial instead of a feast then the proper for the saint, from the Office is used, while the other parts come from the weekday cycle.
Suppose it is not a saint's feast day? Then all of the readings, except those from the Ordinary come from the weekday cycle. So if Tuesday May 2 is not a feast then use the weekday. How do you know which of the four Tuesday weekdays to use? It's based on the Sunday reading. If April 30 was the Third Sunday after Easter then it would be the Third Week Psalms, and Tuesday's readings would come from Tuesday of the Third week.
Evening Office is done using the same day as morning readings, unless the day is the vigil of another feast. Saturday evening readings always come from the Proper of Seasons for the following Sunday.
Night prayers have a single week of readings. Two for Sunday, one after the first evening office and one after the second evening office, none listed as Saturday.
So how does one maintain continuity while jumping from place to place? That's where the colored ribbons come in. I mark the week in the Proper of Seasons with a ribbon, the nearest day in the Proper of Saints with a ribbon. The Night Prayers for the day with a ribbon. The Ordinary with a ribbon, etc.