Editing (by the author) can be done using any word processing program. Microsoft Word is what I use for writing and editing, which comes with most versions of windows. Though Open Office is a strong, free alternative for people who don't have word.
Editing (by other readers) is a bit trickier. No software is really going to be able to help with things like plot holes or character development. Even the spelling and grammar feature of most word processing programs is spotty at best. I do think that some paid editing services are legitimate, but I would first try getting friends and family to read it. If they can't help, then consider seeking out a local writing/reading group. Many meet up in local libraries and coffee shops, or can be found through city groups on facebook. I'm sure if you ask nicely you can find someone willing to edit your work.