Both as a writer and as a general member of society, reading comprehension is a super important skill to have.
I think one of the ways that a lot of people get frustrated by how reading is taught in school is that some teachers will focus heavily on very specific details in books, and so you will end up being tested on reading retention rather than reading comprehension. I had a teacher in high school whose reading quizzes were all about random details in whatever passage we had been assigned for homework (e.g., how many minutes did it take for the floodwaters to get from Town A to Town B) rather than on the actual comprehension of the passage. This can make you feel like you can't do reading comprehension or are bad at it, because it's what you've been tested on (especially if you never took a literature class post-high school).
Here are some skills that I think are important for reading comprehension, whether you're approaching fiction, non-fiction, persuasive writing, or anything else:
Understanding the meaning of a sentence in isolation, a paragraph, a section, and the entire piece. That is to say, having the ability to both parse the meaning of a sentence on its own but also understand how a set of thoughts fit together.
A great way to practice this is to try to explain what something means to someone else (can be a real person, a pet, a stuffed animal, whatever). When I'm working with the people who report to me to edit their writing, one of the things I will often ask them is to explain what they're saying in a very simple non-business way. This also works with someone else's writing--can you take what was written in explain or describe it in plain terminology? Can you summarize a chapter or even a book in a few sentences?
Fitting the writing within the context in which it was written or published. If you see an essay talking about women's safety, for example, that phrasing will mean something different depending on who is writing it. It is often clear from the rest of the essay what they mean by it, but it is key to comprehending the writing as a whole to understand the context in which it was written or published (for example, to know whether it is being used as a transphobic dogwhistle).
Can you identify biases in the writing, either through how it's written or what you know about the author or place where it was published? We know some of the biases that will be present in a piece put out by the Heritage Foundation versus Planned Parenthood, even without knowing the author.
Identifying themes or messages in the writing. Some authors and some writing focuses much more heavily on themes or messages than others (for example, a persuasive essay will have a much greater focus on a persuasive message than an encyclopedia entry), but no writing is truly neutral, and themes, messages, or goals (intentional or not) are present in virtually every piece of writing.
You don't need to write a five paragraph essay about everything you read, but it can be good practice to spend a little bit of time thinking about how the piece of writing presents certain information or people. If someone is described as "stubborn" versus "obstinate" or "brave" versus "foolhardy", it gives a sense of the message being presented about this person. if all characters of a certain race, gender, religion, etc. are presented a certain way, you can start to identify the message that the story is sending about that group--whether or not the author intended it.
Maintaining a critical view of information. This isn't strictly reading comprehension as much as media literacy, but I think they are connected enough to include here. Not everything you read is accurate or true, including things that agree with your pre-existing worldview, and the follow up to the three things I listed before is to identify what something is saying, the context in which it is saying it, and the messages it is putting across, and engaging critically with them rather than assuming it's all correct.
To be clear, I'm not saying don't believe science or anything like that, but, for example, a lot of science reporting in major media is kind of awful and misleading, especially in the headlines. If you see a headline that reads bacon always causes cancer, it's important to look at the actual reporting, potentially even look at the study it's citing, and understand what is actually being said, not what looked flashy in a headline.
Similarly, if you only see a piece of major news in one place, particularly not from a pre-established reliable news source (by which I mean something like NBC and not A Partisan Podcaster on Twitter), you need to double check it. That's not to say it's necessarily fake or misleading, but there's usually a reason only one person is saying something happened.
