It's a combination of prediction and reaction. The more you get used to the situations you'll have to encounter the better you'll be able to recognise and anticipate how to adjust your timing. Honestly, I don't know a real method for learning it (beyond the normal "pay attention to what you're doing while you practice and make adjustments accordingly"). It really does come naturally with practice. The only L-cancels you should miss more than a small fraction of the time are the awkward ones where you're not used to the situation and it's hard to tell when/whether you're going to land. For example: when you're doing an aerial that heavily alters your ECB while rising into a platform (e.g. Marth's dair), or with high-hitlag moves such as Ganon's dair, or against Ice Climbers' double shields.
But the thing is, the same hitlag that forces you to L-cancel at a different timing also gives you the additional time to react and adjust your timing appropriately. The L-cancel window is also large enough that you can bias your timing slightly to sort of cover the other options. 7 frames is a lot, often very close to the hitlag of the aerial. The formula is "[unstaled damage]/3+3", rounded down, if you want to work it out yourself. A move that does 12%, e.g. Fox's early nair, has 7 frames of hitlag. Luigi's early nair and dair both have 8 frames.
Also, you have to take into account the fastfall timing too, since the timing of the L-cancel is relative to that. I feel like many (possibly most) missed L-cancels are actually due to missed fastfalls throwing off the timing by making you land later. In fact, unless you're doing something weird like rising onto a platform, the fastfall timing is the only thing that's actually different on hit/whiff, relatively speaking. The L-cancel is always at the same timing relative to the fastfall, because once you start to fastfall you hit the ground at the same rate whether or not you connected with the move.
To be honest, I'm not totally sure how it works. I'm not sure there's an element of prediction involved so much as it's situational awareness and recognition. In other words, you don't have to know what the opponent is going to do, as such, but being aware of their general options means that you can hitconfirm quickly enough to react to (pretty much) everything. That principle applies to a lot of areas, and is a big factor in a lot of struggles players have that can be hard to identify a direct cause for: the less time you spend thinking, the sooner you start acting, and getting used to the situations so you can recognise things faster lets you spend less time thinking. If you play traditional fighters it should be a lot easier since you're already used to hitconfirming things (you do that in Melee too but it's kind of different because you have more time to follow up, so hitconfirming for an L-cancel is probably closer in practice than hitconfirming for a follow up move).
I'm kind of speculating here.
The multiple L-cancel input method does work, though few people actually do it, and it's not necessary. Personally I find it more trouble than it's worth, but if it helps you then it's fine. However, the principle that you can often option select the L-cancel does apply regardless of how many inputs you make, so in situations where you're not sure whether you have to L-cancel at all or not, you can still go for it. Getting used to releasing shield quickly helps you cover these situations without accidentally shielding afterwards, and that's something that should come naturally with time; I'm sure you remember accidentally holding shield after wavedashing when you were first learning.
