There's lots of ways to edit and it's really a continuum, from the editing we do in our head as we type, to a quick read-through we ask of our spouse, to days and months of painstaking labor, pouring over every single word and phrase to find the perfect pairings. (I talked a little about my own process here). And there are different levels of editing, from big picture developmental editing to proofreading for typos and grammar. Knowing where and when to use your resources is essential. I'm going to break it down into three general categories: self-editing, editing from friends, and professional editing. Each has its place, and the more the merrier.
Maybe some folks can write down a story and have it come out exactly as they want it, but not your average writer. Most of us start with a rough draft, a bunch of words that contain the ideas we want to express, but lacking in clarity, continuity, and completeness. It takes a second pass, then a third or fourth, possibly many more, to polish up that rough gem and bring out the true beauty that lies within. But how?
There are actually a lot of ways to self-edit, and different things work for different people, but it's best to understand up front the limitations to the practice. You can never be the perfect editor for your own work because you are too close to it. You know the idea beneath it, your brain fills in any blanks on the page and gaps in the logic. You don't even need to read the text to follow what's happening. Try as you might, you will never see your work through the eyes of a stranger which is ultimately the whole point of editing - to make everything suitable for the reader who comes upon your words for the first time.
One of the things we tend to be the worst at is the big picture. When you read your own work for a second time, you already know the ending - and the middle and the backstory that isn't even on the page. It can be really hard to get a sense of how things fit together for the reader and whether it actually makes sense. What has worked well for me is to write a one-sentence summary of each chapter and see if that lays out a complete story. But to test the basic logic of your story, it's going to take someone else - especially if you write science fiction and fantasy. All those new terms, magic systems, governmental structures, and strange names have to make sense to the uninitiated and the author is just too buried in the world to see it from the outside.
So your self-editing endeavors are often best focused on the writing itself. To start, the more you know about editing (and writing) the better you'll be at it. So study up. Read some books from editors on editing, read some blog posts, follow editors on twitter. Listen when they talk about what they do and how they do it. One thing you'll find quickly is that despite their differences you'll hear a lot of the same things: use active voice when possible, show don't tell, eliminate redundancies, filler words, and cliches. In other words, follow the basic conventions of good writing. If you want to be a writer, you damn sure better know what those are.
So you know the rules, how do you apply that to your own work? A good way is to do it one piece at a time. Take a rule and edit your whole work focusing on that single thing. Maybe start with eliminating filler words (that, very), follow that with cutting filter words (looked, heard, felt), then maybe watch for sentence constructions to make sure you vary things up. If you try to do too many things at once they will all suffer, so spend the time necessary for each aspect. You'll not only pick up more mistakes, you'll learn to spot these as you write and likely will make fewer of them in the future.
Another way to switch your brain from story creator to grammar editor is to read the work backward. Going word by word will help pick out typos, but it misses a lot of grammar issues. I prefer to go sentence by sentence or sometimes paragraph by paragraph. It helps you avoid the automatic tendency to adjust the image of the words into the ideas (f*r 1nstanee, y0u c@n prbably reed th1s sent3nce juzt fime euen thouph its filld wilh mist*kes). In the editing process, you end up reading the same words dozens of times, so switching things up is essential.
Reading words aloud is another option. It's a different process for our brain to concentrate on pronunciation versus meaning, so we often catch more typos and missing/extra words. It also helps us hear what a reader hears in their brain coming upon new words, which can help find awkward constructions or poor word choices. It works to read it to yourself, but I prefer to find a willing audience - not only do I catch things as I say them, but I can also gauge their reactions (or comments) to get even more feedback. Which brings me to the next editing method:
Editing from friends
Before we talk about different types of 'friends', let's distinguish between having someone help you out as opposed to paying a professional editor in your field. We'll get to the pros in a bit, but it's important to realize that if you're not paying someone to edit for you, you're not likely to get the same effort and results. Even if your friend is another writer, even if they have a degree in English Literature, what you get is feedback from a friend and not professional level editing. (Even if they are a professional editor it's unlikely they'll commit the same time and energy to helping someone for free that they would devote to a paying customer.)
Most often writers will turn to other writers for help. I've exchanged work with a number of different writers and gotten some very useful feedback. (A series of posts on critiquing starts here). Writers (at least the decent ones) should know the basics of writing and be able to apply them to your work with a more detached perspective than your own. Some of it will be personal preferences and stylistic choices, but writers tend to be good at catching regular patterns - do you overuse dialog tags? use the word 'just' too often? ask too many rhetorical questions?
With any editing, it's important to know how much to weight the feedback you receive, and exchanging works can help you judge another writer's strengths. Do they have elegant prose? If yes, then listen to their wording suggestions. But if you don't like something about their style (and we're all hypercritical and judgmental, so it's likely to happen), then take what they say with a grain of salt. You need to write with your own voice and be true to yourself.
The best way to get the feedback you want is to specifically ask for it. I know some writers who do great action scenes, so I'll ask them for feedback on mine. Some are really solid on grammar, so I'll ask for more proofreading from them. Others read a lot in my genre, so their take on themes and tropes is really important. As was true with self-editing, if you ask for everything from everyone, you're likely to get a shallow review of many things without the depth and detail that your writing deserves.
That goes for other friends you ask to read your work. I often use friends on family, but even there I ask for specifics. Some are avid readers, some have English degrees, some just have a good critical eye for typos. Genre readers are often great at developmental feedback though they might not know the terms or reasons. They just know it felt slow, or didn't make sense, or had too many vampires. It's up to you to take their vague responses and understand it means the pacing was slowed by too much backstory, the magic system has too many made up words in it, and your characterization is weak because of a lack of variety in voice.
If you do get some help from those who have some sort of training in writing or editing, most likely it's a different style. People who edit academic, business, or legal documents have a whole different way of looking at things. They are often good at catching problem areas, but there's a good chance their suggested fixes aren't what you want in a work of fiction.
The more feedback the better, with the caveat that you can't let it overwhelm you. Limit what you want from each person and take only what you need when they give it, and you'll be able to use it to improve your writing. Follow every piece of advice that comes your way and you'll end up with a hot mess. Accept your friends' help for what it is and use your own knowledge and skills to apply it and you'll be well on your way to a polished manuscript.
While it's true that good writing is at the core of good editing, they are different skills and require different strengths and experiences. Not all great writers have what it takes to be a great editor - and vice versa. So if you want great editing, you're going to have to pay for it.
But keep in mind that giving someone money does not automatically guarantee a great result. Choose your editor carefully. A high school English teacher might edit a lot of work for their job, but that isn't the same as a fiction editor who works on books in the same genre as yours. Steampunk is very different from memoir, literary technique different from fantasy. All editing (and all editors) are not the same.
The best way to judge an editor is to judge their work. Find out what books they've edited. Read them. Do understand that a book is still the product of an author, so even the best editor can't turn crap into gold, but they should be able to smooth it out quite a bit and take the edge off the stink. So read several books and make sure that their style is something you want for your own, that their standards seem to be at the level you want.
Another good way to get a feel for their editing is to have them edit a sample of your work. Some will do this for free, but even if you have to pay it can be best to pay for a smaller chunk to start with before committing to the whole thing. It can save everyone time and you some money.
And money is an important consideration. I do believe that professional editing is the best, but it's not always worth it. If you're submitting a book to an agent or publisher, you shouldn't have to pay for editing - that's something that comes later. If you're self-publishing, there's a cost-benefit analysis that needs to be done. It's not worth paying a couple thousand dollars to edit a book that realistically is only going to sell a few hundred copies (which is all most books do sell). Paying for editing is an investment with risk, so make sure you can afford to lose that money and take that risk before plopping down your hard-earned bills.
I do want to add that editing is not just an investment in that single book. All editing, especially the professional kind, is an investment in your writing. If you really study the feedback you're given and take the time to not only make corrections but understand the cause of your mistake, you will improve your writing. And to me, that's what makes a writer - someone who not only keeps writing but works to improve and become a better writer. Editing is essential to that process, in any and all forms. Find the path that works for you and your story, and never stop moving forward.