I started my own freelance editing business in 2005 editing books. I work for one e-publishing company as an editor, I proofread for a small publishing company, and I do freelance work on the side. I've been involved in writing and national writing groups since 1993, so I have quite a bit of experience in the fiction genre, which is what I edit. My BA is in History, Spanish, and German. Didn't get an English or Creative Writing degree, but I always got As in my English classes.
You have to like reading, writing, and have a very, very good grasp on the English language and grammar. It's a lot of work for not stellar pay. I do it because it pays me just enough to afford my being able to stay home with my daughter. I have noticed lately that it is becoming increasingly harder to find good companies to work for (freelancing) who will actually pay you decent money for your work. So if you get into freelance editing, you'll want to make sure you're very, very good at English. Because if you're not, you'll be dropped like a hot potato. And because of the less-than-stellar rate of pay, you gotta love what you do. You won't get rich off freelance editing. But if you love a good book and you love the English language, then it might be something you'd enjoy doing.
One more caveat: I've also noticed in the 6 years I've been doing this that most of the new people e-publishing and small companies have been hiring now have masters in Creative Writing and/or specific certification for proofreading or copy editing. This might be what companies are looking for now; I got grandfathered in, I think, and the fact that I can tear apart a novel and tell you internal and external conflict, the goals, motivations, and conflicts of the main characters, as well as the black moment and the three-tier development of the story, as well as watching that the characters remain true to form--on top of grammar, punctuation, sentence structure, verb agreement, etc.--is probably why I am still highly desired as an editor/proofreader.