When you edit your own work, you pretty much have the free reign to do whatever you want with the copy.
  Chop it up in parts?  No problem.
  Rewrite an entire section?  Sure.
  Steal its soul and pull its guts out?  Yep, you can do that too.
If you're editing a piece of writing that isn't your own, however, things begin to get a little tricky.
  Since it's someone else's work, you want to retain as much of their personality and character on the text.
  You want someone familiar with the original writer's work to take a look at the finished piece and know that it is theirs.
Proofreading.
 Basic proofing, the bulk of which can be performed with a writing correction software, usually poses no problem.
  Grammar, syntax and similar things can typically be altered without affecting the overall ideas expressed.
Revising for clarity.
 When editing, you will encounter some passages that may need to be updated for clarity.
  In this situation, look to fix the offending parts on their own, staying careful to preserve whatever ideas and concepts have been put forward.
Revising for correctness.
 This part can get a little tricky.
  If some factual information turn out incorrect or an opinion proves inconsistent, you may end up having to change a substantial part of the text.
  The prudent thing to do is to try and write the update in a way that's consistent with the original writer's style, taking extra care to leave out your "voice" from it.
  It's a dicey situation and is one that can truly test an editor's mettle.