Self Study For those attempting to learn through the power of the Internet
I studied on my own for about a year and a half and managed to chant a hymn from Byzantine notation in matins a handful of times. When I moved back to Pittsburgh and started chanting with chanters that chanted from Byzantine notation I learned much more quickly. Teaching yourself is a very difficult way to learn. Prior to teaching yourself you should ask around at all of the nearby churches to see if there is a chanter that could teach you. If you can't find anyone then here are my suggestions to study on your own.
Print the vespers music from St Anthony's monastery and have it bound.
Print the matins music from St Anthony's monastery and have it bound (not used immediately).
Read the background information links on my resources page. Read anything that isn't over your head. If you don't understand it come back to it later.
Listening to good recordings is absolutely necessary for you to learn on your own. I'm working on some recommendations.
Learn the Greek letters that are associated with parallage (ni pa vou...) and ison. Learn them going up and down one, up and down two and so on. The Greek Letter Card games will help. This is important to do prior to chanting on parallage so that you can focus on reading notation and getting the pitches correct instead of having to think about whether you should say vou or ga.
Learn to chant on parallagebut notreading from byzantine notation. I recommend learning the Nightly Ni with hand sings and playing some of the other Ni Pa Vou Card games (these games need to be updated). By learning the Nightly Ni you will learn the intonations for Modes 1, 4, Plagal of the 1st, and Plagal of the 4th as well as learn how zo changes within the Diatonic scale.
Teach yourself to read the basic interval symbols using the Byzantine Chant Manual or the Parallage Phrases and the Phrases' Teachers' Guide. The phrases in the Byzantine Chant Manual are overly patterned and repetitive but the explanations for each symbol are very helpful and it goes through many symbols. The Parallage Phrases are more incremental and their style is closer to that of real hymns. After you learn the Parallage Phrases you can begin learning the Brief Stichera Verses from vespers (not the stichera themselves as they are harder).
Learn the apichimata for the heirmologic versions of the modes. The apichimata on the Colored Cheat Sheet are the intonations that correspond with the first music that I recommend learning (Brief stichera verses from vespers). They come from The Intonations of the Eight Modes from St. Anthony's Monastery. First learn the apichimata on parallage so that you understand how the modes relate to each other. Then you should learn the Greek phrase that is associated with that mode.
Begin studying the Brief Stichera Verses from vespers. I have put the Brief Stichera Verses in order from easiest to hardest. This is part of the Level 2 repertoire. You can read about how to go about studying it there as well as find the Google doc that gives the order that I recommend studying them in. The main goal of learning these verses is for you to master some simple phrases in each mode and for you to be able to switch between all 8 modes easily by using the apichimata.
Begin teaching yourself the martyria for the diatonic, hard chormatic, soft chromatic and enharmonic scales. I made a prototype for a future material, the Martyria & Fthora Cards and so can you! Use the Table of Scales and Fthora as your guide. I also explain how to use this material there.
Study the More Honourable Verses from Matins (from St. Anthony's). These phrases are slightly longer and more difficult that the Brief Stichera Verses but still at the same level (many repetitive pitches, simple rhythms, no fthora).