You can go to this website, it will explain you how
yourdivineoffice.blogspot.com/
Or you can go to this website
divineoffice.org/
Just download the free podcasts, and it will give you a good glimpse of how to pray the divine office.
Basically the divine office is praying the psalms. In each liturgy of the hours (vespers, for example) You just pick 3 psalms from your bible, recite it, end each psalms with glory be to the father, and in each day, add the magnificat and the canticle of Zechariah. That’s divine office.
Matins (during the night, at midnight with some), sometimes referred to as Vigils or Nocturns, or in monastic usage the Night Office; in the Breviary of Paul VI it has been replaced by the Office of Readings
Lauds or Dawn Prayer (at Dawn, or 3 a.m.)
Prime or Early Morning Prayer (First Hour = approximately 6 a.m.)
Terce or Mid-Morning Prayer (Third Hour = approximately 9 a.m.)
Sext or Midday Prayer (Sixth Hour = approximately 12 p.m.)
None or Mid-Afternoon Prayer (Ninth Hour = approximately 3 p.m.)
Vespers or Evening Prayer (“at the lighting of the lamps”, generally at 6 p.m.)
Compline or Night Prayer (before retiring, generally at 9 p.m.)
I have heard that the book you bought is rather complicated.
This might help you
en.wikipedia.org/wiki/Liturgy_of_the_Hours
The rite you follow is the Liturgy of the hours of Paul VI, the rite I suggested is the old latin rite. I like the old rite better (than morning prayer, evening prayer, etc)