How does one study and improve their tactics?

So, as a beginner interested in improving, I've been reading around a lot on how to get better at chess. One thing I've noticed being recommended consistently by grandmasters and most others rated above 2000 is to focus on tactics rather than openings and such. The argument, a convincing one, is that by learning specific lines rather than improving tactics, you will cave and blunder when a competent player uses a line you're unfamiliar with and have not memorized an answer to. Since it's not possible to memorize every possible line and counter, studying openings as a beginner merely masks the symptoms of the root problem. It is only after this root problem is dealt with that specific lines become relevant, because a win or loss is due more to positional advantages than tactics.

However. the immediately following question which never seems to be explained, is how to learn tactics. How did these grandmasters and exceptional players gain the tactical know-how they possess? How do you gain the ability to competently answer a completely foreign method of attack/defense? Even articles devoted to the topic of tactics only seem to cover it superficially.

Rather than wasting time, I want to deal with the root problem as comprehensively as possible.

Well, I'm not talking as a pro or something, but if at very least you learn 2 opening for both sides (1 for each, better 2 for black) you will improve your rating DRAMATICALLY. Then go with tactics. Idk how, just try some book, like "1000 best tactics", look it up on chess.com, there is a guy, he created a post with an enormous list of books, references and so on. But better start with an opening, because tactis are tactics, but you you are getting fu... you understand on the move 5, tactics won't help you much. Try chessable for that purpose. Quick and comprehensive. First time it took me around 1 month to get long with my paramount problem

I used to have a database in the .cbv/.cbh format that I had found on the internet for free; I don't believe it was copyrighted or anything. Richard Schollar, Tactics in the opening. I found that very helpful and whenever I started learning a new opening I would look up the relevant games for that opening in the database to learn about typical tactical mistakes both for white and black. I don't know if this database is still floating around the internet somewhere.
Other than that chesstempo.com is the obvious choice for quality tactical exercises. They also have this endgame trainer which looks very boring and repetitive (endless Lucena Positions) but did really improve my endgame.
Doing chess puzzles here on lichess can't hurt either.
Also, try to find a couple of strong tactical players from the past or present and study, or at least click through their games to see how they demolished their opponents. The more you do it, the more you will become familiar with the tactical motifs and the quicker you'll spot tactics in your own games.
Emory Tate is a good choice. Maybe Zukertort and of course, Paul Morphy....
Sometimes I'll just watch games of random players rated 2200-2400 beating opponents rated 1800-2100. Most often it's tactics that decide these games. It may not be the most efficient method to get better at tactics, but it is entertaining and quite fun to do, which is also important.

Edit: For a more systematical approach: Tactics don't come out of thin air. There has to be the potential for them in the position on the board. Stronger players usually are much better at finding hidden potential even in seemingly dull positions. To get better at this you need to be good at evaluating positions. To understand factors like king safety, material (im)balances, weak and strong pieces, open files, etc; key squares.... The better you understand what is going on in the position the more ideas you'll find and that is the foundation for any tactics.

"""Rather than wasting time, I want to deal with the root problem as comprehensively as possible."""

The fundament in chess (in my opinion) is the skill to visualize the 'force' of the pieces on a chessboard as quick as possible.
very easy example: en.lichess.org/study/IBOdEgX0

It avoids very simple blunders and mistakes and it is one of the basics for pattern recognition and quick calculations.
I guess the best way to start to improve this skill are very simple endgames and simple tactics.
For the opening use the basic principles first and learn from your mistakes.
If quick improvement is very important for you and you have enough money then look out for a good teacher.

May the force of your pieces be with you :-)

In chess you can learn whatever you want but if you don't have skills you won't be very successful. If you have a gun and you don't know how to use it that gun is useless. Of course you need to learn some basic things. But as soon as possible start doing tactics. First you need to read about 'tactics themes' (pins, double attack, skewers, etc. ). Then go to chesstempo and start to practice there.
My final advice: study your blunders. Try to understand why they happen. Investigate their causes. Avoid them as much as possible. If you can't reduce your blunders everything else makes no sense.

Изучить даже один-два дебюта досконально может позволить себе профессионал. Вообще, человеческая память оценивается в 2 Gb, зачем отдавать хотя бы 0,5 Gb под шахматы? Поэтому изучайте общие принципы дебютов.