First, respect the author. Second, respect the reader.
To respect you as author, I work hard not to change the story or the tone — except when something really seems amiss, and then I’ll let you know. As an editor, I’m there to make an author better, not rewrite the book. Period.
To respect the reader, I work to make the story as clear as possible. This means fixing the obvious copy editing/proofreading-type things. It means cleaning up/tightening up the writing — this might mean rearranging a sentence or paragraph for clarity, cutting down on the number of pronouns in a sentence or making sure it’s clear what pronoun is referring to who (or what), and making sure verb tenses make sense.
Finally: I believe the author has the final call on everything, and am happy to work with you to make sure the book ends up the way you want it.
I really like working in Google Docs. The great thing about G-Docs is that suggestions can be made and it’s easy for you, as author, to accept or reject it. You have the final call. But I can also work in Word if you prefer that.