I am creating one post which captures many resources for the Liturgy of the Hours (LoTH), which is sometimes referred to as the Divine Office or Breviary. I will add it to my sidebar and edit it periodically to include other resources in an effort to keep my sidebar clean. Priests and religious pray the Divine Office with variation based on their individual rule, as do many secular orders. While monastic orders may pray a more full range of hours, many secular orders pray Lauds, Vespers, and Compline. Increasingly, apostolates are adopting this prayer. Many ordinary lay people who discover the beauty of being in communion with the many around the world are also increasingly offering praise to God in this way.
For those unfamiliar, a basic understanding may be given at the St. Thomas More House of Prayer website. Also on this website, there a few online tutorials, with audio.
Colin Donovan at EWTN offers a brief overview of the Divine Office.
Dr. Scott Hahn has many links at his website. This is like a mega-mall on LoTH!
Public Lauds Daily at Assumption Grotto
Lauds is prayed Monday through Friday at Assumption Grotto with parish priests around 7:00/7:10, except on certain Holy Days, but usually on secular holidays like Memorial Day, the 4th of July and Labor Day. It is open to all. If you arrive early, like 6:50, you can knock on the sacristy door to the right of the sanctuary, and request to borrow a Christian Prayer book (St. Joseph's edition), which is what we use. It should be returned by placing it on the altar rail, or knocking on the sacristy door between Masses (7:30 & 8:30). Also ask for a copy of the Latin supplement which contains the morning Benedictus (Canticle of Zechariah), and the Angelus which is prayed publicly following Lauds. They don't always have it. Simple prayers such as the Glory be and Our Father are prayed in Latin, and are contained on this Latin supplment, as well. The priest will announce which pages will be used, but if it is the first time for you, ask someone if you can sit with them in order to guide you. Near the front left are a small group of women who are there almost daily. The psalms and the Benedictus are chanted. It is suppose to be right to left, but sometimes with so few people, some just join one side or the other. Mass follows at 7:30am, and is in Latin. Booklets are provided on the railing.
Catholic Online forums has a good section on the Liturgy of the Hours. The first several posts are detailed explanations of the hours, then what follows are many specific questions people have asked.
CantiNOVA also offers a brief explanation of the LoTH, and provides some online music resources for it.
Many Catholic websites will refer you to Universalis. This is a Catholic site, but for those in secular orders, you should use the sources required by your order. Universalis is incomplete in that it is missing things within the structure, such as the hymn, antiphons, and the intercessions. eBreviary.com, on the other hand, has the full Christian Prayer version online, and covers feast days, as well. I have found it to be mostly inline with my St. Joseph's edition. But, eBreviary requires a paid subscription to daily use. If you want a sampling of what the LoTH is like, they offer several things that are open to all, such as Compline - the prayer we say at bedtime.
I have also found a print edition of the General Instruction of the Liturgy of the Hours. The online edition can be found in my sidebar under Lituryg.
When To Pray Lauds & Vespers
Lay people are not canonically bound to pray the hours in the way that a priest or religious is, so it is good to pray the hours, even without following the rubrics completely. However, by learning the rubrics as best we can, we find yet one more opportunity to build virtue. How? Anyone who prays the LoTH, has likely run into that desire to continue doing something and not breaking stride in order to pray at a specified time. However, when we stop one thing, in order to pray for 15-20 minutes, then resume our work, we not only show God that He is first, but we tame the will. The will should not work us; we should work the will. The same applies to morning prayer and the discipline that may be needed to get up a few minutes earlier, or to place it before all other activities so it doesn't get lost in the shuffle.
On this very subject, Fr. John Hardon SJ, has a wonderful article entitled: The Divine Office as a Form of Sacrifice
Here is just a sampling of time-related questions answered:
Finding Time
Lauds for Laity
Work Schedule
A note about this last one. I asked Fr. Perrone not long after I began praying the LoTH whether I could just say Vespers before I went to bed, along with Compline. This would be around 9:30 or 10:00pm. This is very different from the question above which combines Compline with Vespers (earlier). Fr. Perrone encouraged me to say Vespers when it is meant to be said, around 6:00pm give or take an hour or so. Charity, of course, must always rule, so there are times when you may need to shift, or skip it altogether. But this should be the exception and if it is not, could indicate some changes need to be made in order to fit things in where they ought to be.
Lauds is canonically around sunrise, while Vespers is around 6:00pm, or around sunset (which varies by season, hence the 6:00 recommendation). I have seen various ranges, which are reasonable, but cannot find the link right now. I'll edit this post when I find a good source, so check back.