Explaining is one of the most annoying parts of any magical system, and I never buy into not explaining. When I think about magic systems that interest me, there's always at least some level of basic explanation. I think one explanation I once heard was that by giving the reader the rules of the magic system, they can then start to imagine and predict how it could be used to get out of a situation creatively, like trying to put together the pieces of a mystery. In a similar vein to things like sports anime, if you consider the rules of the sport a magic system and the players the people who use magic, you have to figure out how they're going to beat each other within the rules of the game, rather than an asspull. And similarly, you have to figure out how to explain the rules of the game, but no one ever says "don't explain the rules of the game" right?
And, I think to continue with the sports analogy, I think the best way to explain things is as they're doing it. Continuing with sports, you know the rules of the game and the techniques used, so as long as no one breaks said rules, the reader can go back once something has been explained and go "oh hey, they've been doing that from the start" which is always cool.
For my own, some of it is easier to do organically than others. For instance, everyone in my story just has an animal following them around that will every now and again use magic and the animal symbolism is strong, but of course getting to explaining they're half of your is a bit trickier. The story starts at an Awakening Centre and one of the first major beats is an awakening of a main character getting their symbol, so naturally it's easy to go from "you have a symbol" to "so you're a [insert what I eventually name them here]" and having to leave the centre and naturally from that comes his experimentation with his newly awakened magic, so as he learns so do we. The problem is, of course, doing is organically. Classrooms are so over done and cheap excuse to info dump. But I think combat, if possible, is a lot better sort of place to do it. You can see the limitations and abilities of the magic system in action.
For instance, one of my favourite, and underrated series Chronos Ruler, used the passing of time, either slowing or speeding up as the main "magic" to control their chosen medium. They say this pretty bluntly pretty early one, and because the rule is simple, it's easy to follow. Then take us to our mid-season finale. The main character in particular used playing cards as his medium. We know that he can speed up and slow them down, but we also know the lady he's fighting has the ability to undo his time control, so what does he do? He has a layer of stopped/super slowed cards, hiding/holding back, a layer of super fast projectile cards, so when she undoes the stopped cards, she gets hit with a surprise attack. And because we know the rules, simple as they are, you then go "ooooh that's really clever". Similarly, A Bastard Magical Instructor which as mentioned I take a lot of inspiration from in the actual mechanics of the system, you can tell shit gets real when the MC requires an magic stone and his spell has several more layers than anything we've seen before. When Extinction Ray is firm seen, it's longer and even pointed out within canon to be "wow a seven layered spell" and something that simple says yeah that's something powerful (also that it's called Extinction Ray but you know) and special because 7 layers.
So yeah, I think the answer to how is simply as possible, or in action, and the when is all the time without actually saying anything.