The easiest way I've got to explain level 1 skillchains is that it's rote memorization like multiplication tables from elementary school. So it's best to come up with a mneumonic device that your brain likes to remember.
It's also helpful to note that any level 1 SC that gets made is just the same as the level 1 closing SC property. Level 2 SCs always result from entirely different elements, with the exception of Gravitation containing darkness(compression).
Let's look at the chart, and I'll try to give you my line of thinking that helps me remember:
Transfixion(Light) shines in the darkness(compression), through the waves(reverberation), and brings cold water to the land(Distortion made through Scission).
Compression(darkness) swallows up the radiance of the stars(transfixion), and is moved by the cosmic wind(detonation).
Fire(Liquefaction) is lost under the dust(scission), but becomes a flagrant inferno when struck by thunderbolts(Fusion made through Impaction).
The land(earth, Scission) plays host to raging flames(liquefaction), torrential floods(reverberation), and violent vortexes(detonation).
Calm waters(Revereration) freeze(Induration, ice), but may also conduct electricity(Impaction, lightning).
The fierce wind(Detonation) is brought to heel by lightless void (Gravitation made by compression), and is frail against the mountainside (Scission).
Ice(Induration) may be crushed(Compression, compressed), fragmented(Fragmentation), or impacted(Impaction).
Lightning(Impaction) brings fire(Liquefaction) and the winds(Detonation).
-- Without all the parentheticals --
Light shines in the darkness, through the waves, and brings cold water to the land.
Darkness swallows up the radiance of the stars, and is moved by the cosmic wind.
Fire is lost under the dust, but becomes a flagrant inferno when struck by thunderbolts.
The Land plays host to raging flames, torrential floods, and violent vortexes.
Calm Waters freeze, but may also conduct electricity.
The Fierce Wind is brought to heel by lightless void, and is frail against the mountainside.
Ice may be crushed, fragmented, or impacted.
Lightning brings fire and the winds.
And as I recall, I coulda swore there was a Vana'diel Tribune entry or something like it that went into the nuances of Skillchain research, and how it was the latent energy coming off weapons during the release of the energy surrounding weapon techniques. And iirc, it tried to explain skillchain chart in a flowery way as well.
I will admit, it does get tricky with Triple Property WSes, including Prime WS. In my own experience though, it seems to be that the first and third property are the easiest to interact with, while the middle or second property only interacts if the first or third don't. Examples being:
Origin > Savage Blade = Light and vice versa. Origin's third property of Fusion always interacts with Fragmentation primary property of SB regardless of order.
Origin > Impulse Drive = Induration, while Impulse Drive > Origin = Fragmentation. You'd expect since Origin opening leaves Fusion at the end to interact with Gravitation, that you'd get Gravitation, but no... Reverberation the 2nd property takes precedence, so you get Induration.
You'd think from the Savage Blade interaction that primary property of Level 2 would interact first in every available SC interaction, but it doesn't, as shown by the Impulse Drive example.