Strictly speaking you can't edit your own work, you can only revise it. An editor edits.
As I am/have been an editor, I can tell you how I do it, though.
I much prefer to work from a printed copy because I find I spot more and work for longer that way.
The trick is to work from big to small.
I read through the book, all the way through, and make notes as I go on a separate notebook. I'll not try to resolve any issues in this read-through but can't stop myself correcting punctuation, spelling, etc., as I go. But this read-through is primarily to spot big problems like continuity errors, plot holes, structural issues and so on.
Once I've got all my notes down I organise them a bit: for example, I might have noticed that there's a problem with plot line one which causes issues in three places throughout the book, so those three notes go together (I sometimes type my notes out, but more often I just number them so all these three would get the same number). And then I work through them and fix all those big problems, crossing the items off my list as I go. This stage often involves writing new scenes, deleting scenes, combining scenes etc.
Once all that's done I do another read-through, again taking notes, and again I then resolve all the issues I've found.
I do that until I am happy with the book.
Then I read through looking for smaller things. At this stage I improve characterisation, the flow of the text, etc. I tend to delete paragraphs and sentences at this stage, rather than whole scenes. Again, I read through and only do the correcting once I've finished that read through.
Once all that is done I know I have a ms which is solid in terms of plot, etc. But as I've changed so much in it it's probably full of typos etc. So it gets another read-through and this time I correct as I go, checking spelling, punctuation, grammar, etc.
And once all that's done it gets another read-through, again checking for smaller errors.
And yes, that's a lot of reading through but it's how I was taught to do it by the lovely publishers I've worked for, I've not yet found a reliable method which gives a cleaner ms for any less effort, and it works for me and lots of other writers I know.
