I've never edited someone else's story before, but I've helped some friends on checking their essays/papers to offer an insight on their writing. Though, of course, I'm not a pro.
There are times where I only do a quick check before and after posting my chapter, but when I'm doing a serious edit, I'll end up with several draft folders.
I usually go like: write the entire series freely, then let it sit for at least a week before jumping in to read it with other fonts (sometimes I use comic sans lol). This first edit phase includes more research and plot fact check. I usually write down what's happening within the chapter to compare it with other chapters. Then, I'll come back to chop the chapter (if I were to post it online) and/or any other editing (synonym, sentence flow, etc). After that, I might go for a forth edit or post it!
I don't edit on a first draft. I'll copy every chapter go another folder before making a major edit. For minor edits, though, will join the last draft of edit available.