The internet has made resources available that take all of the guesswork (and a lot of page flipping and ribbons) out of the process. The Liturgy of the Hours is available online here. I find it helpful to mark the text when working with a new group, so that everyone knows when to speak: Leader, Reader, All, etc. Other groups mark up a breviary with ribbons. If a breviary is used, the parish hymn board can be changed to a Morning Prayer board during the week, with breviary page numbers posted in the sequence in which they will be used, so people can mark up their own books.
Expect a small but stable group, whether meeting before or after the morning Mass, or at Vespers time. Some parishes have Sunday Vespers just before the last Sunday Mass, which might draw a larger crowd and can be done with greater solemnity, perhaps with a deacon or priest presiding. However it is done, the Liturgy of the Hours is a prayer experience that can be provided for very little trouble, is almost certain to be successful in a small way, and is properly liturgical.