I'm no stranger to editing. I've edited work, my own and that of writer-friends, on many occasions. Last year, I completed an Editing Certificate from Simon Fraser University. To get the ball rolling, I read some articles on approaches to editing and reviewed some of my class notes. Then I exchanged my 'writing' hat for an 'editing' one.
1. Structural Editing - assessment of the big picture - deciding if any reorganization is required
Using an outline helps a great deal when it comes to structural editing. If you didn't use an outline or an outline isn't provided, then creating one as you do your first read-through can be beneficial.
2. Stylistic Editing - improving the work to make it easier to read and understand
This is the point where specific replaces abstract, and active voice replaces passive voice. Look at word choice (employ appropriate and necessary) and construction of sentences and paragraphs. You can use a quick search in Word to identify the telling and overused words.
3. Copy editing - fixing grammar, spelling, and punctuation - adhering to a style guide (house style or a recognized guide like The Chicago Manual of Style)
Use a style sheet to note unusual spellings or personal choices regarding numbers and capitalization. If you aren't provided a style sheet, then creating one during the first read-through will save time later.
4. Proofreading - one last chance to polish your piece and catch any errors - at the publishing stage, proofreading also ensures final design and typeset is consistent and error-free
This is a very simplified overview of the editing process. Refer to a resource like editors.ca for a detailed listing of the professional editing standards or a professional editor for more specifics.
In doing a self-edit, in addition to the general areas to review, you may see a pattern of your common errors. My first drafts are usually riddled with passive voice and more telling than showing. Writing your story is only the first step in a lengthy process. Your first draft doesn't have to be perfect. That's what editing is for.