During the Wednesday audience by Pope Benedict XVI on praying the Psalms.
Finally, the Pope explained that, in the course of his catechesis dedicated to the Psalms, he had sought to focus on those “that reflect the different situations in life and the various attitudes we may have towards God. I would like to renew my call to everyone to pray the Psalms, to become accustomed to using the Liturgy of the Hours, Lauds, Vespers, and Compline. Our relationship with God can only be enriched by our journeying towards Him day after day”.
One of the authentic renewals in the aftermath of Vatican II is a greater emphasis on the laity praying the Liturgy of the Hours. While it was never restricted to priests and religious it seems to have been seldom practiced by the laity. Though devotions like “Little Office of the Blessed Virgin Mary” a kind of stripped down LOTH was common enough. I myself started with this “little office” and after incorporating it into my daily prayer life moved up to the 4-Volume set of the Liturgy of the Hours which I bought one volume at a time. This has remained a daily practiced from before I officially entered the Church and is part of my rhythm of life.
The 4-Volume set can be imposing for some with the multiple ribbons and the various hours and multiple page changes. Though each year they print a guide book that tells you the page number for the hours of the day and this quickly helps a beginner to start.
Nowadays I simply use the Liturgy of the Hours on my iPad which makes praying the hours dead simple. There are versions available for iOS and Android such as iBrievary which is free and Universalis which is a little pricey. There are also other websites that help you do the same.
Like all devotions in the Church they are not for everybody and so your mileage may vary when it comes to the LOTH. Though I would strongly encourage people to give it a shot even if you start with only reading one of the hours each day. They are so chock-full of the Psalms you can hardly find a better daily devotion. Being immersed in the Psalms each day is a very good thing. Plus I really enjoy the Office of Readings which takes you through the scriptures, the Church Fathers, writings of the Saints, and other Church documents.