I pretty much edit the same way, Cia. At least I do now.
When I first started writing here it was pretty much a quick run through spellcheck and then post **what was I thinking!**
Reading the chapter/story backwards may sound an odd thing to do, but it's shocking the number of things you can find. I sometimes found I had events happening with no build up at all, and even worse I sometimes found that a build up actually led to no event happening The first few times you try it it is so disorientating, but it's a very useful tool to get into the habit of using.
I do a lot of self-editing (sometimes five or six times) before I even send it to a beta/editor. To borrow from our own Louis, always send your team your best work and never your first drafts. For a 5k short story, my recent anthology story went through a total of fifteen edits and rewrites.
I have an online subscription to Chicago Manual of Style, which I have found to be helpful in times of need. However, there are a few editing manuals produced by both Oxford and Cambridge that are useful for UK members, as there are a few differences between US and UK styles.