What follows here is my own understanding of philosophy. I use various terms as convenient labels. Other philosophers have other things to say about the subjects I discuss here; feel free to read them to find out their own thoughts.
To illustrate the fundamentals of philosophy, I'm going to explain my understanding of pragmatism, phenomenalism, scientific naturalism, and utilitarianism. I'm not going to discuss aesthetics; although enough philosophers have written about aesthetics to make it a proper part of philosophy, I personally don't consider it a philosophically important topic.
Before anyone every studies philosophy, or even starts thinking abstractly, we somehow acquire the intuitive concept that there's a "real world" that is "out there," i.e. somehow outside our minds, a "real" world that we discover, not invent, and to which our thoughts do or do not correspond to. As philosophers, we want to explore this intuition. Why do we have it? Which parts of this intuition must be taken on "faith," and which parts have some sort of logical relationship to what is taken on faith? To explore this intuition, I will first create an arbitrary language game called pragmatic scientific naturalism. The rules are interlocking, so to make sense of some rules will require later rules.
The first rule of this language game is called phenomenalism. Phenomenalism (as I define it) states that subjective experiences as experiences are brute facts and strongly properly basic. A brute fact is a foundational fact; it is "true" just by virtue of existing. Strongly properly basic means that the "truth" of a fact is by itself without any mediation sufficient ground or cause to know the fact (and to know we know the fact, and know we know we know, ad infinitum), and that something is not a brute fact is by itself sufficient ground or cause to know that it's not a brute fact. (Weakly properly basic includes only the positive connection. We cannot by definition be ignorant of a strongly properly basic brute fact; we can, however, be ignorant of a weakly properly basic brute fact.) Note that this definition is transitive, and the order is unimportant: that we know a brute fact is "true" is sufficient ground to believe the brute fact is "true."
Phenomenalism says nothing at all directly about any relationship between our experiences and the "real world." Indeed, phenomenalism does not take the "real world" in any sense as a foundational brute fact or as strongly (or even weakly) properly basic. All phenomenalism states is that our subjective experiences as experiences are "true" by definition.
The second rule of this language game is called pragmatism. Pragmatism (as I define it) states that we can think in different ways, and some ways of thinking "do a job" we want done. Pragmatism is weakly properly basic: if something does a job, we can know that it does the job, but we can be ignorant of other ways of thinking that might do the job equally well or better.
Pragmatism says nothing about the metaphysical Truth of a way of thinking; it does not say that because some way of thinking does one job or another that it is therefore True. It just says that we can tell directly that some way of thinking does some particular job.
The first job we're interested in doing is organizing, interpreting, and predicting our experiences. One way of doing that job that we can tell works is to hypothesize the existence of a real world outside our minds with independent "existence" that (somehow) causes some of our subjective experiences, and we can make theories, i.e. connected collections of hypotheses, from which we can deduce statements about our experiences, which we can strongly properly basically relate to our actual experiences. This method works so well that it has actually evolved; we didn't really have to think it up. Our brains just do it for us automatically, but we could, in theory, perform this process consciously with finite minds and no neural pre-processing.
Note that formally, we don't say that there "really is" a real world out there; it's just a useful way of organizing and predicting our experiences; indeed, the two statements are pragmatically indistinguishable, and thus, according to pragmatism, are just two different ways of saying the same thing. If metaphysical uncertainty bothers you, pragmatic scientific naturalism is not for you, but I don't see much alternative than to simply define yourself to be metaphysically True.
tl;dr: Our subjective experiences are obtrusive, and the "real world" is a hypothetical construct that we can tell does the job of explaining, organizing, and predicting our obtrusive subjective experiences.