(for Danya. Totally ironic that you are asking me for advice because this was the part of Carmelite Life that I hated at first! It seemed so boring, repetitive, and pointless! Now it is one of my favorite parts of the day.)
The Liturgy of the Hours is a set of prayers and Scripture Passages that the entire world wide Catholic Church prayers at different hours of the day. You'll be praying the SAME prayers as the Pope and your local parish priest. (In fact, I've got a picture of my smiling Cardinal Wurel above my prayer station because I love remembering that I'm praying with him!)
There are a ton of graces that come from praying "with" the entire Church in the privacy of your own home. I love discovering new Saints and vivid explanations of Scripture passages which always seemed mysterious and remote.
The longest and most important part of the Liturgy is called "the Office of the Readings." These are two long passages which come from either the Old Testament, the New Testament, or writings from the Saints. You can pick which time of day you want to read the "Office Readings". Most people do them first thing in the morning. Then you sing a hymn, read some Psalms and say some intercessory prayers.
As a Carmelites, my husband and I pray Morning Prayer and Evening Prayer. (We're encouraged to pray Night Prayer before bed but I personally haven't yet established a stable bedtime routine with so many young kids in my house.)Meanwhile, priests and Religious pray all the prayers, which are something like six times a day.
a) First find a Liturgy of the Hours book. The prayers are available free on line. I really enjoy praying with an actual book in my hand instead of reading from a computer screen. This is the complete set of 4 books for the entire Church Calendar year at a decent price. We bought each of our books one at a time for around $45 dollars each from the National Shrine. (A new book will be starting for Lent & Easter). Make sure you've got a little "cheat sheet" that tells you where to turn for Feast Days and Special Saints Days.
If you'd like to start in the "baby pool", check out the a single condensed version called "Shorter Christian Prayer:Liturgy of the Hours." for only $11. This is a simple, four week cycle with special readings for Easter and Advent. You can learn to swim easily without getting lost. It will build up your confidence and insure your $160 prayer book investment won't set unused in your bookcase.
b)grab a "Liturgy of the Hours Partner" in your house. Hopefully, Hubs. This type of intense prayer time is like training for a marathon--WAY more fun if you practice with someone else.
c) pick a specific time to start praying. Start with a time to do Office of the Readings each day. Go slow! This is a prayer marathon, not a prayer sprint. It's not about rushing through the entire six prayer set in one day. It's about slowly building up a feasible prayer schedule for the rest of your life.
d) be strategic about WHERE you pray. I usually pray on the living room couch with my husband. We are "available" to little babies in need. I've discovered if my kids can see me praying, then they usually don't interrupt me half as much as if I'm hiding in a closet trying to get my quiet time with Jesus.
d) be flexible. Life is going to get crazy and you're going to fall off the Liturgy prayer schedule. We are not in a convent. We have messy, needy, unpredictable people in our lives. Be gentle with yourself and remember this prayer schedule is "optional for lay people." At the same time, when my life was REALLY falling apart I clung to this prayer routine. It's a solid rock under your feet in times of sickness, stress or fear.
If anyone has more helpful hints, be sure to chime in!