My blog posts so far have mostly been about how to edit. That holds true for most every other VN editing blog I've ever seen as well. But I'm a really big believer in approaching any significant task from a "Why, What, How" perspective. So now, let's try to answer those first two questions.
Even "What Is Editing" would be starting in too far (it made for a better title, so sue me). Let's start with this: why do translation projects, or even original fiction projects like novels, have editors?
The goal of editing is to help the author achieve their goals.
An author brings a whole lot of goals to the table: a story, characters with personalities and motivations, a setting, overarching motifs, style, ... probably a lot of other stuff I forgot. Anyway, you get the idea; there's a lot there which they're just trying to get out on paper (or bits, or whatever) and then into your brain.
An editor doesn't bring any of that stuff. An editor instead strives to understand all of these things the author wants to communicate, finds the points where they can be better achieved, and refines the text to better achieve the author's goals. Although there's obviously some overlap, there are quite different skill sets involved in the raw writing and the editing, and thus the two roles are often fulfilled by two people.
How about for a translated VN, rather than for, say, writing a novel? The story is roughly the same, actually. Although the translator has essentially the same goals as the editor in this case, the skill sets required are quite different, and thus differentiating the two roles is not uncommon and frequently beneficial to the project, for the same reasons as it is with original writing and editing.
I'll also add that an original writer is usually considered "too close" to the original text to make a good editor. Even a writer who is also a great editor will benefit from having someone else edit their manuscript. I haven't heard the same thing said of translators, though, so that might not be relevant to this special case. But the skill set differentiation point still stands in the case of translation.
Assuming you're satisfied with that explanation for Why, let's move on to What.
Professional manuscript editing typically distinguishes four kinds of editing: developmental editing, line editing, copy editing, and proofreading. Those are ordered based on both the scope of changes they make, and also the chronological order in which you should do them: developmental editing is very macroscopic and happens first, while proofreading is very microscopic and happens last. Let's drill into each:
Developmental editing is, first, the act of identifying all of those authorial goals I mentioned, and second the act of cutting, rearranging, and adding large chunks (think: add this whole new scene, cut that whole character) in order to advance the author's goals.
Obviously, that second half isn't applicable to VN translation. You're not going to cut whole scenes or change how characters behave. Those decisions have already long since been made by the original writers, hopefully with the help of an editor of their own ;).
But the first half is essential, and is quite a bit harder in VN translation, since you generally can't actually talk to the writer. Read it all, understand the authorial goals, and build a strong, consistent interpretation of the plot, the characters, the motifs, the setting, the tone, everything you can think of. If you don't form an interpretation while translating/editing, you're liable to thwart the author's goals as part of your translation, and as a result accidentally obscure or entirely lose key points of the original intent. Of course, you'll occasionally make mistakes in your interpretation, resulting in mistakes in translation. But if you don't even form an interpretation, the result will actually be worse: you'll still make mistakes in the translation, and the resulting translation will certainly be internally inconsistent, but you won't notice those internal inconsistencies because you have no guiding interpretation. If you form a consistent interpretation and let it guide your translation, when the text goes against your interpretation, the resulting inconsistency means you'll notice it, correct your interpretation, and then go back and modify your translation to fit the corrected interpretation.
Line editing is about assessing and fixing the flow of a scene and the flow of a line. It's about logic, language, word choice, rhythm, the mechanics of a sentence, and the sound of human speech. It is not concerned with grammatical errors, punctuation, and spelling, but more with higher-level ideas like tone, emotion, and atmosphere. A line editor worries whether a sentence ought to be punchy or loquacious, not whether it has all the commas in all the right places.
"Logic" probably seemed a bit out of place there, so let me give an example for that one in particular, since it's essential. For example, unless you're editing the VN equivalent of a Beckett play (and if you are, please point me to that VN, because I'm interested), one dialog line should generally be a logical response to the previous one. A canny line editor will ensure the logical flow from event to event, line to line, and even scene to scene, ensuring consistency of the narration.
This is also where all that authorial intent mentioned above comes into play: an editor in this capacity should also be ensuring consistency of a line with those overarching goals. A good line editor will help ensure that characterization is consistent, for instance, or that a motif is not buried inappropriately. An editor, in their avatar as the keeper of consistency, is crucial to achieving those authorial goals.
The prose side of line editing is also key simply because stilted speech, unnatural utterances, redundant repetition, awkward alliteration, and their ilk all kick you out of the immersion. Your brain wants to keep reading something when it flows well. And nothing hits softer than shitty prose.
Line editing is the meat of VN editing. It's what most existing VN editing blogs are about, not coincidentally. If you're an editor for a VN, line editing is what you should be thinking about constantly.
In addition to recommending other VN editing blogs, notably Darbury's blog (mostly about line editing, though all the punctuation ones are more about copy editing) and Moogy's now-ancient blog post (basically all about line editing), I'll also suggest you go read up on line editing in a general setting. A quick search for "what is line editing" will lead you to mountains of useful links. As a random example, this is one such useful link, and it's hilarious, well-written, and edifying: http://www.thereviewreview.net/publishing-tips/short-course-line-editing. There is a veritable sea of such articles on the internet. Read them.
Copy editing is about the nuts and bolts of grammar, punctuation, and spelling. It's not the same as proofreading, but it's getting close. The copy editor typically should select and enforce an appropriate style manual (AP, Chicago, MLA, take your pick). The copy editor is the person who gets mad when you write "I baked 7 blackbirds into that pie." instead of "I baked seven blackbirds into that pie.", and who calmly, patiently replaces all your misused hyphens in the middle of sentences with em-dashes.
You're unlikely to have a dedicated copy editor on a VN project; if you've got the "editor" role, you're probably it. I think this is along the lines of what most people think of already when they hear "editing" anyway, but really the line editing is the most important to the enjoyment of the text. Still, the picky people among us can get awfully uppity if you start putting in stuff like ellipses with four dots and inconsistent use of the Oxford comma (sidebar for the attentive: I'm for it, as you've already noticed). Copy editing is a particularly thankless job, since it's not like you can do an exceptional job of copy editing and really salvage a bad manuscript, but poor copy editing can certainly hurt an otherwise-good manuscript. So it's worth investing the time in doing it carefully.
One important recommendation for copy editing: take notes and build up a style document and glossary for your VN as you go. Are honorifics being used? What about name order? If you're going to romanize some words, is your romanization consistent? Do you 1) always write "senpai", 2) always write "sempai", or 3) mix and match? I don't care if it's 1 or 2, but it better not be 3. Write conventions like this in a shared document and make sure everybody knows about the conventions and the document.
Proofreading is the final stage of this pipeline. The role includes checking for grammatical errors, spelling errors, punctuation errors, typos, and perhaps some more exotic things like incorrect English dialect. It's straightforward and mechanical. Like copy editing, it is essentially thankless. It is, nonetheless, important. While you're making big sweeping edits doing all the stuff above, you're going to create tons of errors at this level. They need to be fixed. Make sure you have someone (preferably not the "editor", because they're too close to the text) do a proofreading sweep. You can lump it into QC if you like, but make sure that whoever is assigned to do this is looking at it carefully. Check. Every. Single. Word. There are errors in there, I guarantee you, and they're embarrassing. Getting the number of errors down to near-zero before you release your translation is going to make both you and your audience happier.
There's not one editor; there are four. In an ideal world, with original fiction, you'd actually have someone separate filling each role. For a translation you don't need a developmental editor, leaving you needing three editors. In the non-ideal world you live in, you've probably got at least two of those roles to yourself. Push for someone else to handle proofreading, at least (call it "QC" if you have to), and make sure said person has the necessary ability and attention to detail. If you're the "editor", then you're almost certainly doing both line editing and copy editing. When that happens, make sure you keep a balance amongst all the things you need to do: for instance, spend 10% of your effort trying to understand what the author is trying to achieve, 88% of your effort on line editing (it's the meat, after all), and 2% on copy editing the little details like punctuation, romanization, etc.
And If You Can Only Remember One Thing
Focus on line editing.