Arcade games are simple; by and large their basic mechanics are designed to be understood within seconds. As a result, an introduction to shmups or arcade gaming in general does not necessitate a 44 page pamphlet or longwinded essay. So cutting to the chase, if you're already interested in arcade games, here's generally how to best approach one:
1. Your first goal is the one credit clear (1CC). If the game loops (repeats), your goal is a one credit clear of the first round. This is considered by most serious players to be the baseline criteria for "beating" an arcade game.
2. Don't use continues for a while. Just see how far you can get on one credit. Make single credits starting from the beginning the bulk of your play time, as this encourages consistency and is also more fun than slogging through the game continuing over and over. You can get pretty far just doing this, and indeed some players only do this and have cleared lots of games.
3. When you start hitting a wall, a really tough part that you always die to and just can't seem to crack, ask for help, or watch a replay by a skilled player, or use a practice mode if available, or use savestates to practice small sections, or all of these things. The objective here is to get a clear strategy for the thing stopping you, but try not to get too bogged down in "practice."
4. If the game has a significant scoring system, incorporate scoring strategies as desired, but your first goal is to clear by any means necessary. Don't worry about scoring a part of the game if you can't survive it.
That's it, really. Download MAME, grab some roms, find a game that clicks and have fun with it.
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With that out of the way, I'd like to share some of my reasoning for these guidelines. The first arcade game I took really seriously was Tetris The Grand Master, which is particularly conducive to the habit of only playing full runs. There are MAME cheats that will fix the level for you, and there's clones of the game out there where you can set whatever speed you want, but for most players "training" outside of just playing the game over and over is minimized compared to the habits of many top western shmup players. This is because TGM is basically all execution and no memorization, so practice at a particular speed does not confer the benefits of say, using savestates to develop strategies for part of a stage in a standard action game with more fixed obstacles; there's no real reason to do almost exactly the same thing as playing a real game but without the possibility of achieving a personal best. I started with this game, and so it was hammered into me from the beginning to do full runs, develop consistency across the whole game, and improve slowly but steadily.
A good reason from an improvement perspective to prefer "full runs" over isolated practice in all arcade games is consistency. With sustained practice you start to take for granted that you can do the easier parts without any trouble, until you start doing full runs again and it turns out you can't. Consistency aside, the crux is that it's simply less exciting to soberly plug away at a savestate, practicing and devising with nothing at stake, instead of spending most of your time playing games that begin at the beginning and end when your credit ends. There is no adrenaline rush in taking a section from 10 minutes into a game and doing it over and over again in isolation, versus doing it in the heat of the moment with your run on the line. Yes, you might fail and lose your credit and have to start over because you don't know what to do, but that's the point. This is where the excitement comes from: when it's the Real Thing and you're out in the deep end without a clear idea of how to handle what's coming up, that's when the survival instinct kicks in and you're alert, on your toes, being forced to come up with a plan on the fly. And as a matter of fact, quite often, really solid and memorable plans come out of that.
But I've been there. When you're going for the basic 1CC, and you've dumped two or three dozen hours into a game, patiently playing credit after credit with minimal assistance, and you've reached the final boss like ten times, yet you fail each time. At some point the frustration and temptation becomes too great and you need some kind of sure plan. Your continued enjoyment of the game is at risk, but to just drop it would be the epitome of dissatisfaction. Here's where I would look up a replay, bust out a savestate and just get the damn thing nailed down before trying again. No shame in that. But to, as some suggest, break the game down into savestates from the jump and practice each part in isolation as a kind of exercise apart from actually playing the game, seems incredibly tedious, and the suggestion of which I believe turns off prospective players. To become good at these games, says these players, you practice it. The game must become work. I don't want to deny that some folks actually enjoy playing the games in this way, or to insinuate that they should stop doing so, but I want to get across that it's not the only way to get good at an arcade game. It may not be quite as "efficient" to do mostly full runs but to use a tired cliche, it's about the journey, not the destination. The more time with a game that's filled with exciting moments the better, right?
A little bit on scoring: I believe, by virtue of it being easier to survive than score, it's better to go for survival first and completely ignore whatever scoring system there is for the most part (i.e., Use The Damn Bombs). What helps alleviate the supposed eventual tedium of doing the first couple of stages in each credit is that you can integrate scoring tricks naturally as they become easier to survive in, but there's no sense in playing too risky to get a good score on later stages if you're not already familiar with how not to die in them. You might succeed and get a good PB once, but you're much more likely to hit a wall because the maneuvers you're using are probably harder to perform.
I feel like this is a nice balanced approach to take to arcade games, to treat them as exciting action games instead of some weird puzzle box to dissect, while allowing for the occasional assist from outside resources to keep your interest from waning when you're stuck for too long. I doubt any genuine noobs read this entire essay section but if you did I hope it wasn't completely impenetrable, as this is years of my built-up slight dissatisfaction with the arcade community finally being expressed. Anyways while you're here, yes, use autofire if you want. Everyone does it, no one will judge you.