It really depends on the kind of writing you want to edit.
Academic editing is a very different creature from literary editing, and business editing/corporate communications falls somewhere in between them ...and too often falls right through that crack into sad oblivion.
Books and websites are great, but I strongly recommend that you attend a writers’ conference (preferably in the writing discipline you want to edit, but at this beginning stage that’s not essential yet) and arrange to meet with other editors and agents there. Go to their workshops, sit with them at lunch, offer to buy them coffee, and ask them questions… and write down their answers. Use your smartphone to record the conversations with them, if they don’t mind (they won’t mind). What they say will make perfect sense to you in that moment, and five minutes later will evaporate from your brain, believe me.
Anyway, since you asked specifically for sites and books, here are some I’ve found perennially helpful:
• the Purdue University Online Writing Lab (Purdue OWL)
• Grammarly. ...the site itself, the app, and the browser plug-in. It won’t always discern the context correctly, so don’t slave yourself to it, but don’t ignore it either. It will catch a lot of dumb stuff you don’t want to slip past you.
• Polishing the PUGS (Punctuation, Usage, Grammar and Spelling), by Kathy Ide - a handbook to keep nearby all the time, better than Grammarly because it trains your brain so you don’t need to rely on Grammarly so much, to catch the “dumb stuff you don’t want to slip past you.” And besides, sometimes Grammarly gets annoying and you have to turn it off; or a client will ask a punctuation question that stumps you.
• Kirszner & Mandell: The Brief Wadsworth Handbook. Absolutely required for every academic writer and academic editor. You are running the academic race with your ankles shackled together if you don’t own this manual. Get the edition that’s comb-bound so it lays flat at any page, with tabbed dividers to jump straight to the section you need at that moment. (…and by the way, if this thing is the Brief version, I’d hate to meet the Full version in a dark alley.) (Update: editions published after 2012 or 2015 or so seem to be called The Pocket Cengage Handbook—that's the same thing!)
• Kick-Ass Copywriting in 10 Easy Steps: Build the Buzz and Sell the Sizzle, by Susan Gunelius. Yes, it’s written for marketing and advertising copy (“copy” here means “writing that has to fit in a certain place”, like “ad copy” and “web copy” etc.). But advertising is simply English writing that has to be as carefully crafted as possible, for maximum effectiveness: good ad copy is like fine scotch, strongly distilled and irresistible to its intended audience (but possibly nasty or offensive or overwrought to everyone else). The skills needed to refine normal English into a compelling sales pitch are exactly the skills needed to be a good editor for other purposes, especially business communication.
• Story Engineering: Mastering the Six Core Competencies of Successful Writing, by Larry Brooks. James Scott Bell, Randy Ingermanson, KM Weiland, William Zinsser, Donald Maass, and Sol Stein have also written many excellent books about fiction writing that apply to everything from flash fiction to the epic novel series. You can go deeper into the Hero’s Journey and all that mythic stuff, but Brooks, Bell, Ingermanson and Weiland make it practical and applicable. Brooks manages to squeeze it all into one thick book; Bell, Ingermanson, and Weiland spread it across several books & articles & online courses that make it more accessible piecemeal.
So, those are some starter books for Academic, Business/Nonfiction, and Fiction editing (and writing too, since they are dance partners at the Great Party of Publishing Wisely), plus the one reference book and some digital aids to help you edit common PUGS problems. Now for just one good book specifically to equip you for the editing task, the editor’s role in the dance: okay, here’s two, because fiction and nonfiction really are that different.
FICTION: Self-Editing for Fiction Writers: How to edit yourself into print, by Renni Browne and Dave King. I know of no better beginner’s resource. Read this book analytically (see Mortimer Adler’s How To Read A Book if you don’t know how— don’t feel bad, most people don’t), then get into a conversation with Dave and Renni, they give their sites & contact info in the book, which is an open invitation to, well, contact them.
NONFICTION: Thinking Like Your Editor: How to Write Great Serious Nonfiction— and Get It Published, by Susan Rabiner and Alfred Fortunato. This is the kind of book that Pulitzer-Prize-winning authors call “the standard text for serious nonfiction writers for years to come.” It speaks very little to the aesthetic aspect of writing, leaving that to the entire rest of the how-to literature on writing. Instead, it focuses on the kinds of questions editors ask of the books and authors they edit, the kinds of questions that lead to substantive and aesthetic changes that dramatically improve the book, but which are inspired by pragmatic and strategic, not aesthetic, reasons.
It also happens to be an interesting read. In fact, all these books are a pleasure to read, except maybe the Brief Wadsworth Handbook, which is more like a pleasure to refer to: it’s the difference between a surfboard and an ejection seat. Although that makes it sound like I’m constantly bailing out of my academic fighter jet… Never mind. You asked for books & resources to help you learn editing skills, both “comprehensive” and focused on “common (i.e. mostly basic) mistakes. This is my best shot in the short time I have.
I hope this was helpful! Let me welcome you into the editing world!