I think the place to start is with the consciousness that all media is a collection of choices. All of it. Everything that is in a piece of media is a decision that someone made, from the big themes to the individual pixels on the screen in a video game, those are only there because someone made a decision that caused them to be there.
With that as the foundation, you can start asking the needful questions.
I find a useful place to start asking questions is “why X rather than Y?”
In any given piece of media you want to analyze, pick a choice that is being made and imagine what it would be like if a different (or opposite) choice had been made.
Say, in Star Wars, what if Luke had decided to join his father and overthrow the Emperor? If the movie had made that choice, how would it have changed the film? What would it feel like is the point the movie is trying to make then? What if Vader was not Luke’s father?
Or, what if the good guys’ lightsabers were red and the bad guys’ sabers were blue? What does that change? What are the things you instinctively associate with those colors, why would swapping them around feel wrong? (or would it actually feel really right? If so, why?)
You can do this for the very big questions, like themes and entire plots, but you can also do it in the very minute. Read a poem and ask yourself why the author picked this word rather than one of its synonyms. Maybe it’s for the meter, maybe it’s for the tone, maybe it’s to match vocabulary. Imagining a different word or a different phrase in the poem, how would that change how it feels to read? What it feels like to hear it spoken out loud?
The answer to many questions you’ll ask about a piece of media are entirely banal. Like, in 3D animation, some things look the way they do because that’s just how a particular software suite handles that particular task. Light reflections, physics simulation, motion blur, etc. Plenty of video games look the way they do in no small part because they are built within the constraints of their engines. Sometimes paintings have the colors they do not because an artiste is imbuing every choice with profound meaning, but because those are the colors the painter could afford, or which were available at the time. And those banal answers are still useful, even if they don’t sound deep.
But the important bit is, the more questions you ask (however banal), the more answers you’ll learn, and the more you’ll understand about the mediums you’re interested in, and the more you’ll become able to interpret the choices that are made and work towards building an understanding and constructing a reading.
If you start from the understanding that everything (everything! literally every single thing!) in a piece of media is a choice, a decision that could have been made differently, and you ask yourself why it wasn’t, you’ll be in a decent position to start to interrogate the art you enjoy.
Outside of that, there are lots of books on art appreciation, and tons of people doing videos on media literacy on YouTube. I think Crash Course has some high-school level courses in English and Theatre and Film on their channel, which can be another good place to start.
Also, just, generally… Media literacy is a skill, not a trait. It’s a thing which you practise doing, and in practising it you inevitably become better at it. Nobody starts out good at it, literally everybody is improving with practise all the time, and literally the only way to get any better is to try to do it to the best of your ability as much as possible, working the muscle so it will start to grow.