All the people you talked to are correct in their piece of the puzzle. It's simply just watching your opponent and taking mental notes on what sort of things they like to do. How they recover, how they tech, how they escape danger, how they DI, how they edgeguard, what they do in neutral game (this one is big IMO - take a look at what weedwack said), etc. And as you notice them doing a certain thing, you can try to punish it, and you will learn what works against certain actions and what does not. So not only do you have to learn to notice people's patterns, but you have to learn how to defeat the patterns that you observe, which will come with experience and experimentation. Sometimes it may be difficult to punish a certain action even if you know exactly what they're going to do.
This next part is talking more about how to improve reading opposed to how to read, but...
Bear with me, but if you've ever taken a Psychology class, you may have learned about the "hidden observer" of your mind. An example is driving. A lot of times your "conscious" mind will be thinking about things completely unrelated, and you aren't even consciously paying attention to the road, and yet you can drive just fine. It's like another person is doing it for you. Your autopilot.
Well, you can come to the point where your "hidden observer" automatically takes in information about your opponent without you even thinking about it. For me, I often know what my opponent is going to do a lot of the time after a game or two (especially worse players), even if it feels like I barely payed attention.
But you will probably have to consciously observe at first. Don't be lazy, and consciously force yourself to take mental notes on your opponent's habits in as many friendlies as possible, especially vs people nearish to your skill level. And the more you go out of your way to do it consciously, the better you'll be at it automatically (I have gotten pretty lazy with this and play on autopilot most of the time these days, but I used to make myself do this a lot).
And when I consciously read these days, it's like, my hidden observer is still helpful - because I consciously notice some things, but my hidden observer notices some other things without my realizing. They work in conjunction to take in more information than I could just consciously. Kind of sounds weird when I put it in words but yeah.
OK I probably went a little overboard there because the bottom line is "practice reading consciously", which seems pretty obvious. Didn't really need to explain the result. But IDK, as obvious as it seems, there's a lot of people in this community, where I literally punish the same thing over and over the same way and they keep doing it. So it feels like a lot of people play on autopilot all the time and never improve their reading ability. They try to improve their combos, edgeguards, tech skill, whatever, but not their reading. Reading is a skill like any other and requires practice to improve.
Dunno how helpful this will be but I tried, so yeah, good luck.
