I never had whatever it is that it takes to try being a PUA, or Pick-Up Artist, but I did get obsessed with them for a while and did a lot of reading (as is my wont).  I've grouped them into a handful of types:

Angry PUA: "Women are worthless and stupid, and I will fuck them."  The focus is on crude manipulation and bullying.  Will travel the world to find economically disadvantaged women.  Growing more popular by the increasing-inequality minute.  Exemplar: Daryush Valizadeh (aka Roosh V).

Creepy PUA: "I will be your perfect lover."  The focus is on painting romantic pictures, hypnotism, neuro-linguistic programming, and mirroring.  Losing popularity because it's too "beta", and also because it's creepy.  Exemplar: Ross Jeffries.

Fun PUA: "Let's have a good time."  The focus is on enjoyment, conversation, and denying serious emotions.  Some of them actually enjoy themselves.  Exemplar: Later Wayne Elise (aka Juggler).  Some of them use relaxed enjoyment to paper over bottomless pits of self-loathing and anger.  Exemplar: Jared Rutledge (aka Holistic Game).

Robot PUA: "My 53 step plan leads to sex 67.8% of the time in field trials."  The focus is on empirically testing what set of buttons to push on women in order to get sex.  Exemplar: Early Owen Cook (aka Tyler Durden).

Self-help PUA: "Men should get less validation from sex, and more from self-improvement."  Most PUAs with a brand end up here eventually, once they've grown older and realized that the constant pursuit of sex didn’t make them any happier.  This is also when (no doubt coincidentally) many of them start saying things like, “I no longer identify myself as a PUA.”

What do they advertise as the best way to control women, and does the PUA use negging?

The Angry PUA attempts to make a woman feel shitty about herself; he deploys heavy doses of negging.

The Creepy PUA attempts to make a woman feel floaty about romance; no explicit negging here.

The Fun PUA uses the culture of chill to convince a woman her feelings aren't important; negs are subtle, and chill girls can take a joke, right?

The Robot PUA uses rapid state changes to convince a woman she's feeling something; neg-compliment-demand-dreamyeyes-neg-excitement.

What's the importance of other men?

The Angry PUA depends on other men to help maintain a culture of dependent, needy women.  He wants to be seen as a manly man by other men.

The Creepy PUA laser-beams his attention on women.  Unless other men are either lauding him as a poet or beating him up, he mostly ignores them.

The Fun PUA attempts to be a social magnet, attracting both men and women.  The goal is to have other men vouch for him as the life of the party.

The Robot PUA will push buttons on men, too, if it leads to more sex with women.  Depending on the training environment for the Robot’s machine learning routine, this may lead to an Angry Robot, a Creepy Robot, or a Fun Robot.

How can culture make it easier to control women?

Angry PUA: Economic inequality, insecurity for women, and male anger.  (Perfect for right now.)

Creepy PUA: A flood of "romantic" films and books, repression of sexuality.  (Welcome to the 1980s, or the 1780s.)

Fun PUA:  Chill.  (Only goes out of style during Good Wars and tent-meeting revivals.)

Robot PUA: Sociopathy that thrives in an anonymous world of one-time interactions.

No woman is an individual to a PUA, but more experienced and creative PUAs of each type have a wider repertoire, which can make it more difficult for women they approach to recognize that they are in a simulacrum of an interaction.  For example:

A beginning Angry PUA has a handful of general-purpose negs to go with his barely-disguised disdain for women, while an advanced Angry PUA digs for a woman's specific weaknesses and uses them to undermine her self-confidence and destroy her sense of agency.  An advanced Angry PUA aims to have multiple pliant women who serve his whims and whom he can abuse freely.  Some Angry PUAs naturally become Men’s Rights activists.

A beginning Creepy PUA can spout romantic clichés as he awkwardly stares at you, while an advanced Creepy PUA takes women as his creative muse; he’s a Byronic Don Juan with a poem or painting or song for every woman.  An advanced Creepy PUA aims to have multiple women deeply in love with him.  Some Creepy PUAs make a big deal of being feminists.

A beginning Fun PUA has a couple of entertaining stories, while an advanced Fun PUA is an improvisational raconteur who can read your grocery list and make it sound like an adventure.  An advanced Fun PUA aims for multiple fuck buddies and a group of guys who think he’s great, all of whom are simultaneously chill and ready for a good time.  A Fun PUA doesn’t care what your politics are, as long as you’re not uptight about them.

A beginning Robot PUA might suffer a kernel panic if an interaction goes off script, while an advanced Robot PUA has many decision tree subroutines to personalize your experience.  An advanced Robot PUA aims for an increasing mathematical ratio of anonymous sexual to non-sexual interactions.

Beginning PUAs have varying mixes of fear, anger, inadequacy and desire for control in relation to women:

Angry PUAing appeals to the man’s anger and desire for direct control.  The Angry PUA tries to demean a woman and destroy her feelings of self-worth in all arenas except her pleasing of him.

Creepy PUAing appeals to the man’s fear and inadequacy.  The Creepy PUA tries to create overwhelmingly positive emotions in a woman and avoid any hint of anger or negativity from her.

Fun PUAing tries to tone down all heavy emotions and enforce light-hearted fun.

Robot PUAing denies all emotions in the Robot PUA while trying to create an emotional whirlwind in the woman.

The Self-help PUA tries to get men to separately work on their fear, anger and feelings of inadequacy in addition to working on their Game, and promises that more sex will follow as a side-effect of more positive emotions - but if you let your success (or lack of success) in sex impact your emotions, they say, it won’t work.

There are a couple of types that I haven't thought about as much, but they deserve to be mentioned.  The Gimmick PUA says, "Watch my magic trick!" and is exemplified by Erik von Markovik, aka Mystery.  The Style PUA says, "I wear a fedora," and is exemplified by Neil Strauss, aka Style.  Both of them offered a grab-bag of routines, tips, tricks and style advice.  Strauss, of course, wrote a book.  (He eventually transitioned to Self-help PUA, and then wrote another book.)  If there’s a stylistic quirk (e.g. the dreaded fedora) or a complicated word-for-word pickup routine that you associate with an invasion of PUAs, it probably comes from the trick bag of one of these guys or the many imitators who gathered around them.

The Burning Man Spiritual Polyamorist (exemplar: Ian MacKenzie) didn't come from the PUA community, but I'd argue they share an approach with Creepy PUA, updated for a new age.  They both claim to offer women something higher and better and purer than sex (romance for the Creep, art and spirituality for the Burner).  They both "really get to know a woman, deeply, the way she truly is", while somehow never managing to see the actual woman in front of them.

The book Intimate Connections is sometimes mentioned by PUAs, and it covers about 70% of standard PUA advice.  The author uses different labels, but the concepts are there: "inner game", "cold approaches", "peacocking", "shit tests", "be the prize".  Even "negging" shows up, in the form of Burns' recommendation of the "insincere compliment".  However, absent from the book are the PUA world's misogyny, anger, objectification, and encouragement of rape culture.  When Burns talks about "the game", he says,

You play the game, not to 'win' or to put someone down, but to have the chance to share your life with someone in a deeper, more genuine manner.

He separates himself most clearly from PUA thinking when he says,

Other people aren't just extensions of your ego, they are separate and unique and have minds of their own.  It may be a pleasant fantasy to believe that if you behave in just the right way you can make everyone love and desire you, but the world doesn't work that way.