I II VI isn't a very common chord structure. Basically, when you speak of scales, you speak of intervals... The 3rd, the 5th, the 7th, etc. But, there are chords that fall within this scale pattern that are chords that work with every particular interval of the scale. Except, they are called degrees in order to differentiate between notes (intervals) and chords (degrees). The roman numerals are usually used to indicate the degree. And, it all really comes down to the I being the starting chord that reflects the key (major/minor). It is simple and hard all at the same time. But, once you understand it, it is only simple. Basically, if you are starting in a Major key, you start with a major chord. Usually, to make it work perfectly, you use 4 tone chords (the ionian being a Maj7). So, you start with a 4-tone major chord and then move each each voice of the chord up 3 intervals. That will give you your next chord. And, you keep doing this and eventually after 7 chords, your eighth (octave) will be the same exact chord that you started with. Except, it will be one harmonic (octave) higher.
The reason why it is advisible to use 4 tones is that you are including the most common extention... The 7th. The 7th is what helps to identify the "dominance" of a particular chord (though, working in triads can also show you dominance, it just isn't as , ahem, extended) So, a major scale using chord degrees is as follows: I=Maj7, II=min7, III=min7, IV=Maj7, V=7, VI=min7, VII=half diminished (min7b5) and then back to I=Maj7, except it is an octave higher. To do the same with a minor key, you just start with a minor chord or a minor7th and move each voice of the chord up 3 intervals. Pretty easy.
It is a lot easier if you write the scale down in notation. But, do not write it linearly. Write it as if all the notes in the scale are a chord. write all of the notes within a chord across the entire staff (not just the number of notes in the scale, write them all the way across the staff). Then, start with your major chord and count 3 intervals up on every voice and you will arrive at your next chord. In notation, you will be able to see the note relationships right on paper in front of you. It is quite a revelation. This system is what is used to harmonize your chords and it is used to determine what chords get what voicing in what degree of the scale. It is very useful for constructing the chordal structure of a song depending upon what chord progression you are using. And, as for progressions, those are usually in a formula of 4ths and 5ths. I IV V, II V I, etc. All progressions are variations on 4ths and 5ths. And, the chords used in those positions are typically chosen from the degree system that I have described above.
You can look at any piece of music and see these patterns. It makes one ask what really is new in music. The answer is that there is nothing really new. It is all just recycled with different emphasis on particular notes. Essentially, it has all been done before. Here on FP, though, the focus is on the beat. Which, is a much more simplified take on the recycling of music. It relies on the rhythm rather than the harmony and melody (though, those are present in a simpler form). Sure, it can be quite complex. But, nothing in any particular style of music has not been done at some prior time. So, emphasis is the key to breaking apart. How you stress a note in that common pattern of what our ear likes to hear.