These days PUA refers to so many things that I need to be more specific. The sources that helped me were "The Mystery Method" by Mystery, "How To Become An Alpha Male" by Carlos Xuma, "Married Man Sex Life" by Athol Kay. I would also recommend "The Blueprint Decoded" by RSD.

Yes, there are many sources that only tell you "do this, do that, and if it does not work, just do it again". I guess this is what most customers want: "Don't bother me with explanations, just give me a quick fix!" This is how most people approach everything. Well, if there is a demand for something, the market will provide a product. And these days it is a huge business. Ten years ago, it was more like geeks experimenting and sharing their results and opinions... a bit similar to Quantified Self today, just less scientific, and sometimes more narrowly focused.

Overcoming aversion to rejection, doing many approaches to convert given rates of success into greater absolute numbers, doing something extraordinary to stand out of the crowd... those are the fixes. Applied incorrectly they could be even harmful. (Receiving a lot of rejection can make you more resistant, but can also break you. Standing out of the crowd is costly signalling, you need to pay the costs. Doing many approaches may cost you socially.) But there is a theory behind that, and maybe it is not clearly explained, maybe it is not emphasised enough, or maybe it is already obvious to many people, and only a relevation for the most clueless guys like me. (Actually, maybe the explanations are not in the books, but in the related blogs. I don't remember the exact sources of information. I am only sure that "Married Man Sex Life" contains the theory explicitly.) And I guess for a LW reader familiar with status and reductionism, another part is already known.

Here are a few useful ideas; the essence I got from the books and blogs, but the result may be a compilation of various sources, with a bit of LW lingo --

Humans are biological creatures. Attraction is a causal mechanism, not an unexplainable mystery. That does not mean there are no individual preferences. But the shared preferences are also important, and hugely underestimated.

Sometimes the society gives you wrong explanations, for various reasons: People fail at introspection. People optimize their answers for status, not for truth. The inferential distances between socially savvy and socially clueless is too big, so even a honest and good advice gets misunderstood and misapplied. To some degree, sexual mate selection is a zero-sum game, so there is an incentive to spread bad advice. The social advice is optimized for the needs of society (e.g. preserving the social order), which may be misaligned with your needs (e.g. getting from the bottom of the pecking order to the top). -- Of course, if we go more meta, the PUAs also have incentive (status, money) to give you bad advice. Caveat emptor; just don't make this a fully general counterargument.

Reproduction strategies of males and females are different. Some things are universally attractive (health, intelligence), but some things are sex-specific, or at least have different weight for each sex. (Yeah, the mandatory disclaimer: Not all people are heterosexual, even the heterosexual people are not all the same, etc. Just don't miss the forest because some trees are outside of it.) The specifically male preferences are widely known (all those half-naked ladies on the covers of magazines didn't get there by accident). The specifically female preferences are somewhat less known. Why? Consider the incentives: Women prefer to keep this mysterious, because mysterious means higher status. (This is why any attempt to explain the mystery feels like a status attack.) Men who understand them have no incentive to teach it to their competitors. And the men who want to learn, must first get a huge status hit by admitting that they need to learn. (Even worse, the status hit is guaranteed, but the good advice in return is not, and most likely one will not get good advice.) This changed with the internet subculture of low-status males, where admitting to strangers to be low-status does not cost one socially, and thus the usually taboo topics may be freely explored. (With the commercialization of PUA, the status games are back again.)

Specifically: to most heterosexual women, high status men are attractive. A lot of advice is about getting higher status, or about faking some signals that high-status men send. (Actually, getting higher status or faking it, is not a dichotomy. Sometimes status is in the eyes of the beholder: if you convince people that you have high status, you have it. Also, faking the high status can make you more confident, and when you learn to be confident, you will get high status naturally.) Wise people will remind you that becoming a high-status male will also help you in other areas of life, unrelated to seduction, so perhaps instead of becoming better at seduction you should frame it as becoming better at life. -- Add some specific tricks and fixes here, and you have a typical PUA material.

Problem is that the typical PUA material is optimized for short-term relationships. For someone starting from "no relationships" position, that is a huge improvement. But to get a long-term relationship, another lesson has to be learned. Some male traits are attractive for short-term relationships, some male traits are attractive for long-term relationship. The official story says they are the same, which is wrong (but socially useful). Reversing this stupidity, a typical PUA in a valley of bad rationality says they are opposites to each other, which is also wrong. In reality, they are approximately orthogonal. For short-term relationship you need "alpha" traits: to be strong, successful, healthy; in other words, to show you have good genes. For long-term relationships you need "beta" traits: to be kind, reasonable, faithful; in other words, to show you would be a good father. These are not the same, and these are not opposites -- when you fully understand this, everything else is just a commentary. Statistically, young women will put more emphasis on "alpha" traits (which is why PUAs focus on that), but as they get older, they realize the importance of "beta" traits. Men are socially pressed to develop "beta" traits, because that is the part society needs; but having only "beta" traits without "alpha" traits does not make a man attractive.

This is the root of most misunderstandings: When a man asks: "How to become attractive?" he often means that he starts from zero and cannot get even a short-term relationship; which means he needs to work on his "alpha" traits. However, a women hearing this question will typically interpret it as: "How can an already attractive man become even more attractive?", she imagines a typical attractive bad boy, and recommends adding some "beta" traits to that. This is why this kind of communication predictably fails, and then it leads to endless flamewars about whether women really want or don't want "nice guys". The answer is: Women want attractive men to develop "beta" traits; but there is a silent assumption that those men already have "alpha" traits. Women don't want men with zero "alpha" traits, regardless of how much "beta" traits they have.