Essentially there are three editing phases: substantive editing, copyediting, and proofreading. It's highly unlikely that you'll find an editor that does all three. In fact, you might be wise to run away from someone that offers to do all three stages, because:
You may be familiar with the basic types of editing already, but we'll recap just to make sure everyone's on the same page.
Substantive editing is what I call big picture editing, and it can change your manuscript for the better. Assuming your editor knows what she's doing.
Substantive changes include things like reorganizing paragraphs, sections, or even chapters to improve how the story is told. Your editor may also suggest that you scrap sections that don't move the story along or rewrite portions that impede the flow of your work.
When your editor is done with the substantive portion of your revisions, there's a good chance your manuscript will look very, very different. That's why this is generally done first, before any copy editing or proofreading.
Copyediting is next. (You may also hear people call it line editing.) Once the big kinks in your manuscript have been worked out, an editor will move on to sentence-level changes, keeping an eye out for problems with grammar, spelling, and punctuation. For most fiction works, The Chicago Manual of Style is the reference of choice.
This is the time when your book may get a style sheet too. As you can imagine, editing isn't an exact science. There's room for someone to make a few judgment calls. For instance, in a non-fiction work there may be multiple spellings for a particular location. If neither is wrong, you must pick one and stick to it for consistency's sake.
Likewise if you're working on a non-fiction book, this is the point where facts, diagrams, charts and captions will be thoroughly checked for accuracy. Other fiction manuscripts, like works of historical fiction, may be fact-checked too.
During this stage the proofreader will check a sample (or galley or ARC) of your book for errors. While she may find spelling or punctuation errors that fell through the cracks in the copyediting phase, she's also looking to make sure the book meets layout and styling specs. In addition, the proofreader may check the current revision of your book against another version looking for any changes or omissions.
Hiring the Best Editor
Now that you know the differences in types of editing, it'll be much easier to find the right editor for your project—at least as it exists in its current state. The way to find a good one is to ask yourself a number of questions.
Don't forget to talk with your fellow She Writes members for recommendations on great editors and proofreaders, too!