The Monastic Hours are the original formulation of this liturgy for the Roman Rite and follow the guidelines given by St. Benedict in The Rule. These can be found in the Monastic Breviary or The Diurnal.

The 1960 Hours are the Hours which coorespond with the 1962 Mass. Sometimes these are called the Roman Hours. These often come in a three volume set.

The Divine Office is a term which can be used interchangebly for Liturgy of the Hours. However, most often it is used to refer to the 1960 Hours and/or the Monastic Hours exclusively, omitting the newest version. You will find arguments that the terms are different and refer to older and newer forms respectively. Use your best judgement.

The 1970 Hours are the Hours which coorespond to the Mass promulgated in 1970 after the second Vatican council. This version of the Hours and the Mass are referred to as the Ordinary Form. These can be found in full in a four volume set, or partially in the Christian Prayer book and the Mundelein Psalter. 

Everyone is invited to add their voice to praying the Liturgy of the Hours if they feel comfortable doing so. Below is the format we use when chanting or singing this prayer. Tones/melodies used are found in the Mundelein Psalter. 

Mundelein Psalters and Christian Prayer books are located on the cart which is regularly stored at the back of the chapel in front of the confessional. This cart is moved to the center aisle behind the baptismal font just before a scheduled prayer time.
 

Introduction - Cantor sings the first line alone. Everyone sings the response together. Then the cantor sings the first half of the Glory Be*, and everyone sings the second half together as well as the Alleluia that follows (Alleluia is omitted during Lent).

Hymn - Sung by everyone in unison

Antiphons - Sung by the cantor alone before each psalm and canticle, then repeated by everyone together. Repeated one time again in unison at the end of each psalm and canticle.

Psalms and Canticles - First full line sung by the cantor (intoned). Second line sung together by everyone else (cantor will sing too as needed to give musical support)
Third through final lines alternate between choir one and choir two. If you understand what this means then you may choose to be part of choir one or choir two. If you do not know what choir one and choir two means then you will chant the even lines only (line 2, line 4, etc)

Reading - The cantor will invite someone from the congregation to say the reading. We do not chant the reading at this time. Anyone may volunteer to read by simply beginning to say the reading out loud after the cantor asks. Unlike at Mass, there is no introductory phrase before the reading nor a call-response phrase after. Only say the words of the Bible verse.

Short Responsory - The cantor will sing the first line. Then everyone repeats this line together. The cantor will sing the third line and then everyone will sing the fourth line together. The cantor will sing the fifth line and then everyone sings the sixth line together.

Gospel Canticle Antiphon - Same format as other antiphons

Gospel Canticle - Sung in unison after the cantor intones the first half of the first line

Intercessory Prayers - The cantor will sing both halves of each prayer. After each prayer (six in total), everyone will sing the response together. The response is "Lord, hear our prayer" or a phrase that is similar and always uses the same melody.

Our Father - Sung together using the melody found on page 50 of the Mundelein Psalter

End Prayer - Chanted by the cantor alone. Everyone sings the reply, "Amen"

Concluding Invocation** - Chanted by the cantor alone. Everyone sings the reply, "Amen"


*The text of the Glory Be is different than what is commonly said in a Rosary and what is used at Mass (found in the propers). Both are accurate English translations and in Latin the text is identical. We use different translations for the Hours and Mass because that is what is provided in the offical texts and an individual church is not permitted to change the texts for either liturgy.

Liturgy of the Hours version
Glory to the Father, and to the Son, *
and to the Holy Spirit:
as it was in the beginning, is now, *
and will be for ever. Amen.

Mass Propers version
Glory be to the Father, and to the Son,
and to the Holy Spirit.
as it was in the beginning, is now,
and ever shall be, world without end. Amen.

**The concluding invocation is replaced by a blessing if a priest or deacon is leading the prayer outside of Eucharistic Adoration.

All Hours are prayed in English in the Ordinary Form unless otherwise noted

Tuesday:
6:00 PM Evening Prayer (chanted according to the Mundelein Psalter)
9:00 PM Night Prayer (followed by Benediction)

Wednesday:
7:30 PM Night Prayer

Friday:
6:00 PM Evening Prayer (during Lent only)

iBreviary is available online, Android, and iOS.
http://www.ibreviary.com/m2/breviario.php
This app has all the offices of the 1970 Hours available in many languages including Latin, Spanish, and English. You can download the prayers and the beginning of the day and access them offline later.

Laudate is an app available on Android or iOS. It has many prayers, complete Catholic Bibles, and more. Overall it is a wonderful app; however, for the Liturgy of the Hours it simply redirects you to the Universalis website. This means you have to have your data or wifi on to access it, and you might as well go directly to the Universalis website.

Universalis is available online, Android, and iOS. 
https://universalis.com
This app provides all the offices for the 1970 Liturgy of the Hours.
Free version: The online website uses a non-ICEL translation for the English. This is fine for personal use, or if everyone in your group is using the same app. It can be a problem if some members of your group have a book version or a different app they are using. You will quickly see the meaning is the same but the wording is slightly different making it difficult to pray together.
Paid version: Details on costs can be found on the FAQ page here:
https://universalis.com/n-faq-nothing.htm
You can pay a flat rate that will get you access to the app forever. Or you can choose to pay a monthly rate. The paid version has the same English translation as is found in the 4-book breviary set. The paid app allows you to download the prayers when online and then access them offline. 

Magnificat has an app which includes daily prayers for morning, evening, etc. They state the prayers are inspired by the Liturgy of the Hours. These are not the prayers you would find in the 4-book breviary set. This means this would be okay for an individual to use, or if a group is all using the same app, but it will not work in a group setting with people using different sources. 

Divine Office app is available online, on Android and iOS. 
https://divineoffice.org/welcome
The website and app have the 1970 Liturgy of the Hours. On their homepage they mention having some issues they need to work out concerning copyright permissions. They mostly closed registrations online, but reopened them again to meet the needs of the homebound caused by COVID-19. As of Aug 20, 2020 the app is downloadable for free and does not require registration.

On the app you can play a recording of a group reciting the prayer and / or read the prayer in text. 

All Catholic Prayers does not appear to have anything resembling the Liturgy of the Hours (tested on Android in August 2020)