No one right way

In a post at Pub Talk: Interviews With Literati, Jonathan Galassi of Farrar, Straus and Giroux says of editing: "Editing is something you learn by doing. It’s basically common sense, I think. You watch what your elders do and try it yourself. The proof is in the pudding. You get thrown into it and help the author to produce a coherent whole. There’s no one right way to do it."
He's right, up to a point. Editing is a craft; you learn how to edit by editing.
And yet, let's not make it look too easy. During the years when The Sun regularly hired copy editors, I occasionally got letters of application along the lines of "I thought I might give copy editing a try if I make parole." There are people who think that copy editing is no more than proofreading, putting in commas here and taking them out there, changing that to which and which to that. Thumb through Strunk and White and the Associated Press Stylebook (or more dauntingly, the Chicago Manual of Style) and you're in business, they think.
For that matter, "helping the author to produce a coherent whole" would be a breeze if the author were not, as some are, misinformed, tone-deaf, defensive, and mulishly stubborn.
To the extent that editing can be taught, I have attempted to teach editing to undergraduates for eighteen years at Loyola University Maryland, some of whom have listened when I told them that editing cannot be learned from a book, that they must show up in class, that we only learn how to edit by going over the damn text word by word, sentence by sentence, paragraph by paragraph; only to learn, at the end of fourteen weeks, that they have scarcely made a start on the enterprise.
I myself never had such a course, or any journalism course, for that matter. There is indeed no one right way to edit, and there is no one right way to learn how to edit. But, apart from taking my course at Loyola, I can suggest some ways that you could go about learning the craft, or improving it.
You have to read, widely, constantly, omnivorously. We learn to write as we learned to talk, by imitation, and you need to be familiar with the kinds of prose, formal and demotic, serious and jocular, sacred and secular, that the writers you edit will be imitating.
Similarly, you must through reading build up a fund of widespread general knowledge that will allow you to recognize allusions and that will trip the editorial alarm bell in your head when some statement of fact doesn't look quite right.
You will be expected to be knowledgeable, if not expert, on grammar and usage, and that knowledge will have to be a good deal more sophisticated than the hoary superstitions of schoolroom grammar. Arm yourself with Garner and Merriam-Webster so that, if challenged, you can give informed explanations of your choices and changes.
You will learn to read analytically, and the best way to start is to pay close attention to your own reactions as a reader. When you stumble over a word or phrase, you do not shrug and keep moving, like a pianist who hits a wrong note during a concert. You stop, back up, and examine why you stumbled. When you find yourself bored, you stop to ask why the text is so boring. Part of your job as an editor is to represent the interests of the reader, and your own responses as a reader will steer you toward the problem patches.
Chances are that if you are thinking seriously about being an editor, you have already submerged your own ego and understand that it is not your article or book, but the author's article or book, or the publisher's article or book, and your task is to assist it in achieving its purpose. If your longing is for riches, glory, and the love of beautiful women/men, you have no business attempting to be an editor.
You will, if you have the chance, apprentice yourself, working in some kind of shop with experienced editors, and you will watch them, learn from them, discuss the craft with them.
You will "get thrown into it," because there is no single, simple preparation for editing. You will have to learn from your mistakes, both the minor, "oh, that's the way we do that" oversights and the colossal blunders that will make you cringe in recollection years afterward. Because you will make mistakes. Editing is about making judgments, multitudes of judgments, major and minor, and no one's judgments, least of all yours, are infallible.
You may sometimes get gratitude, though you shouldn't count on it. But you can command respect. And you will have the satisfaction of seeing that faulty has been corrected, the murky clarified, and the ungraceful made more shapely.
Take note always of that inner satisfaction; that is your principal reward.