Once you understand it a bit it goes from complicated to just tedious as hell since you need to plan affixing out over multiple items before going for the final part which is affixing the weapon you want to spruce up. General rule of thumb is that most things need 3 of the same affix to be reliably transferred onto something else or upgrade into the better version of an affix. There are exceptions to this, with specific -Soul affixes improving the affix chance of certain affixes, though for the most part that doesn't matter anymore since Dim weapons have the stat VI affix as their augment factor when you enhance them to +35. The ones that get the most complicated are the Super Affixes (I don't know if that's the actual terminology used by the community or not, but lets use it for now) which are the ones introduced in episode 1-3, episode 4, episode 5 and episode 6.
For the episode 1-3 one (Astral Soul), you can just get a ray or union weapon for weapon affixing instead which helps significantly streamline things (for posterity it takes one Soul of Darkness affix which shows up on stuff from the Profound Darkness fight, along with four Astral Catalysts, meaning you need a bare minimum of 4 weapons/units to make it).
For episode 4's (Aether Factor) you need 1 Aether Soul (combine 2 of the following affixes: Fullvegas Soul, Escarde Soul and Eastern Soul. Or I think it was 2, might be all 3?) and 4 Factor Catalysts (Deus Factor + Mother Factor + Yamato Factor). Fortunately with the release of Ship Infiltration it's a lot easier to make due to certain Lamia series weapons having Factor Catalyst for its augment factor (the wired lances one I believe) and also have 1,2,3 S affix slots. (More on those at the end) Aether Soul is thankfully not too hard to get the materials for, but may require running tokyo/vegas expeditions and possibly Deus/Mother triggers or the Whistle of Chaos recommended quest when it comes up on rotation.
For episode 5 (Mana Reverie) it's one Omega Memoria (Omega Reverie + Historia Soul + Fabula Soul, with the latter being the hardest to come across) and 4 Reverie Catalysts (Elder Reverie + Luther Reverie + Appregina Reverie + Gemini Reverie + Persona Reverie). Omega Memoria sometimes will show up on items dropped by Omega Luther on Ultra Hard and tend to be at 7-8 slots already (for weapons), which may be your best bet rather than try to farm Fabula Souls. Reverie Catalysts have many sources outside of making them yourself while also not being too troublesome to get the materials for considering Persona can drop items with any of the reveries on them. In addition to this, some Lamia series weapons have it as their augment factor along with the Profound and Starquake weapon series, making the super affix Mana Reverie quite a bit easier to make than the rest (though still troublesome on units, but to a lesser degree)
For episode 6 (Absolute Glare) I'm not too sure beyond it following the same formula as episode 5 where there's 3 that combine into one and 4-5 others that combine into the other which you need 4 of total. We can't make it quite yet though, not until we get the last 5 levels of divides.
Now for actually reducing time and resources wasted, there are newer affixes that have an S and a number beside it (I'm not sure if they're called S affixes, but nobody has corrected me yet) that can be slotted into weapons that have a corresponding slot (second tab of the weapon details) and have a 100% success rate to transfer no matter what, which reduces the amount of potential affixes failing to transfer when trying to increase the slots on a weapon for example.
Ultimately it takes some experimentation, but fortunately you can feel it all out without comitting to actually affixing an item by selecting some equipment to affix together, checking how it affects the success rate % and so on.
This is a bit of a hefty read but I hope it helps you make sense of the system.
edit: I spent way too long writing this, holy crap, but still, hopefully it helps someone out there.