"Editing process" is a term I use loosely. I don't really have a unified approach to editing my writing. Part of this is because I write a wide variety of different genres. Another part is that some of my manuscripts come out better in their first draft than others. My path for editing fiction is often quite different than my path for editing nonfiction.
For fiction, a full cycle from first draft to final draft can take years. There are several reasons for this. One is that it often takes me months to complete the first draft of a story. I have a few stories that have been in the works for over a year. Length of story is a small component of this problem. My problem here is that I have trouble sustaining effort on projects until they're done, either because of other work (and subsequent loss of momentum) or because I'm unhappy with the quality of the work-in-progress. I really need to learn to just finish the stories, and I hope to finish my works-in-progress eventually. The next reason my stories take a long time to develop is because I don't like making major changes right away. My first few rounds of editing generally go after problems at the paragraph and sentence levels, avoiding larger problems that aren't glaring. After months of a story lying around I tend to be more apt to making large-scale changes, such as completely rewriting a story from the beginning. Closely related to that second reason, the uncertain endpoint for stories leads them to continue changing over time. Until I've posted a story to my blog or had it accepted somewhere, my stories are stuck in limbo. I make changes every once in a while to continuously improve them.
Most of the time I'll ask alpha and/or beta-readers to critique my stories before I start submitting (and sometimes later). I then use that feedback to make changes. Most of this feedback is small stuff, so I make sure the mistakes are indeed mistakes, then I fix them. For larger pieces of feedback, such as comments about a weakness in a character, I will go through the manuscript and make changes throughout in order to improve my story. I don't take all advice given to me. If I feel that the changes recommended would harm my story either in style or vision, I will ignore them.
My own editing steps often start while I'm writing. Sometimes I fix my stories up as I write them (a habit I'm trying to break); other times I make myself notes for later regarding what I'll need to revise. After my first draft is finished, I let my work sit for a few weeks (assuming I have the time). When my eyes have refreshed sufficiently, I reread my story and note what changes should be made. I will usually fix small errors as I go. After I have a list of changes to be made, I make those changes. After I have my second draft, I read through the story again and repeat until I have my third draft. Then my fourth. Then my fifth. Some of my stories look very similar to their original forms, while others are barely recognizable.
For nonfiction, my editing steps are much the same as my steps for fiction. The main exceptions are that I usually don't have alpha/beta readers and I don't often wait more than a few days before making edits. For something like a blog post, edits often take place a few minutes after I've finished my last sentence. If I were trying to get something published professionally I would probably adopt a system closer to that which I use for my stories. I don't think the changes would quite compare to those that I've made over the past four years for a certain story though. It is also virtually unheard of for me to note future revisions while I write a nonfiction piece.
The way I have written about my editing process may make it seem like an actual procession of actions that I adopt for each piece. This is deceiving. While my process is very loosely the same each time, I don't force myself to use any particular method. Sometimes I print my manuscripts out and write notes on the paper. Other times I do everything on the computer, adding notes in red type within red brackets. Often I take notes with pencil on paper as I read from my laptop. It's a little different every time. For this process I leave a big disclaimer: results may vary.