In order to learn material that is written in the standard system we have to remember that it will be referenced by notes, scales, chord symbols, intervals and roman numerals.
Therefore in order to understand what they are talking about we should have a method of viewing all these ideas in our system.
Whenever a note is referenced without context, then we can always look at it based on it's number representation. So for example if a request to play E is made we can think of that note as 4*.
But the moment we learn more information about the situation we can change it up, so let's say the harmonic backdrop was D* major, then when there is a request to play E, we think of this as an anchored interval 2.
Since we were just talking about D* major, we also need to be able to convert scale types into the anchor intervals they represent against the root of the scale, so when we see major we think 0 2 4 5 7 9 11 immediately.
We should know how to convert an interval in the standard system into a number so a tritone for us is a 6.
Additionally we should be able to take an chord symbol in standard notation like A#minmaj7, and say what relative interval collection it represents, that being 0 3 7 11, if we have set an anchor note, then we should be able to produce the ais generated by this chord as well, so if our anchor note was G# then they would be 2 5 9 1.
As for roman numerals we should be able to know what each of the numbered chords mean and not be confused by the different numberings, so for example the VI chord starts on the ai 5, and the V chord starts on the ai 7. Additionally we should know the process of turning a roman numeral chord into ais, for example the II chord is a minor 7th chord and therefore since that is a chord symbol, we know how to turn that into ais.
On the flip side we also need to be able to communicate ideas that we get from the anchor system to the standard system.
When we're talking about ais we can always extract the note out of it by adding the anchor note back to the ai (which is the reverse process) so if we have an anchor note of 5* and we have the ai 8, then the resulting note is 1*.
In the anchor system there is alot more freedom in the way we build stuff since we're never trying to use a predefined structure when we make chords, so for example if I want a major sound I can just grab 0 4 7 9 2 play them all at once and then enjoy that sound.
To explain that in the standard system, we have to attempt to find a structure which fits it, so for example let's say our anchor note was 2*, then we could say that we've played a D69 chord or we could describe it as a Bminsus7 chord, all we're trying to do is define that ai collection by using structures found in the standard system.
Note: We can describe it as Bminsus7, because if anchor on the 9, that ai collection becomes 0 5 3 7 10 which is the relative interval collection of a minsus7 quality chord.
Given any number we should be able to get the standard name equivalent from it so a 1 is a minor 2nd.