Joe, the Canons exist also in Compline and the Midnight Office as distinct from Matins. And I disagree that they are not a 'devotion'.
In fact they are a uniquely Byzantine form of prayer, whether privately or as part of a more corporate liturgical service, such as Matins, Compline or molebens. I have found these Canons to be of great solace and inspiration in private prayer.
Canons can be prayed privately if one wishes for any of a number of occasions, from temptation to preparation for Communion to prayers for the deceased. Even in the Old Believer usage there were numerous canons prayed by the faithful in private prayer for various occasions in addition to the usual public liturgical use of the canons at Matins, Compline, molebens, etc.
The full Oktoechos has a beautiful sequence of Canons to the Theotokos for every evening at Small Compline throughout the year in the tone of the week outside of times of the Festal Menaion, Triodion and Pentecostarion. These are true masterpieces of liturgical poetry in honor of the Theotokos. Likewise the Canons to the Most Holy Trinity from the Oktoechos for the Midnight Office (Mesonycticon) of Sundays are masterpieces of Byzantine devotional poetry.
Dear Griego, anyone can pray the Canons. Canon comes from the Greek "Kanon" which means rule or order.
If a Canon is to be prayed privately it can be done by saying the usual beginning prayers, Psalm 50 and then the Canon. There is a good outline for praying the Canons on Father John Whiteford's page,
http://pages.prodigy.net/frjohnwhiteford/order.htm The Old Believer prayer book also contains an order for the layman to pray canons or molebens in private or as family prayer.
The Canons form an integral part of Compline and Matins in the Byzantine tradition and are also found in the Midnight Office (Mesonycticon) of Sunday.
The Canons were originally based on Scriptural odes, from the song of Moses at Exodus in Ode 1 through the Song of the Theotokos (Magnificat) in Ode 9. The Canons are some of the greatest and most profound hymnography and liturgical poetry in the Byzantine tradition.
As has been mentioned, a Canon is generally comprised of eight odes, although they conclude with Ode 9 as the second ode is usally omitted outside of the Great Fast. The structure is an introductory irmos followed by troparia and responsorial phrases such as "Glory to Thee, our God, Glory to Thee" ,"Most Holy Theotokos, save us", or "Saint N. pray to God for us" depending on the particular canon. On some days more than one canon is prescribed for Matins.
During weekdays of the Great Fast, the Canon is limited to three odes during Matins, hence the name "Triodion". The three ode sequence is much more ancient than the later eight-nine ode compositions. The nine ode poetic Canons have basically supplanted the nine Scriptural odes, although they are still present as excerpts in some of the liturgical texts of various canons.
Some of the greatest hymnographers of the Byzantine tradition, such as St. Cosmas of Maium, St. Andrew of Crete and St. John Damascene were especially known for their texts of various Canons.
At the end of some Canons is a katavasia, a linking phrase theologically. In monasteries during the katavasia (which means "descent") the choir would literally descend from their stalls to the center of the church where the katavasia were sung.
Canons and Akathists can be prayed jointly, with Akathists following after the first and sixth odes of a canon, seen often in more traditional monastic "cell" rules of prayer.
Akathist means literally "without sitting" or is to be prayed in its entirety while standing. St. Romanos the Melodist wrote the first known text of the Akathist to the Theotokos. There are many, many Akathists in existence.
Speaking of Akathists, we have the "New Romanos" right here on this forum, our dear Alex, who has composed some beautiful Akathists.
Sorry, as usual I rambled on far too long, may God have mercy on me.