I think editing is a vocation more than a career. If you don't have a good ear for your own language, learning to edit effectively is going to be difficult.
I joke that I began correcting my elders at an early age, but it's true. I did. And I gained a lot of experience in all kinds of jobs, always looking for more senior people I could learn from. There's more to editing than memorizing a style manual. You also have to have a tremendous amount of general knowledge, an eye for different authors' prose styles, and an understanding of how to relate to the people you will end up dealing with in this business.
Some editors are joiners (there's the Editorial Freelance Association, for example). I'm not. Maybe that has hurt me, but I can't tell if it has. What continues to be invaluable, though, is participation in the copyediting-l mailing list and some other freelance lists that are not strictly editing-related. Editors compare notes all the time, and I consider copyediting-l to be the main source of continuing education for editors at all stages of development.
You also ask what services I provide. I provide services to publishers of all sizes, but mostly I work with self-publishing authors. I offer all levels of edit (except proofreading and indexing, both of which I outsource); interior book design and composition; cover design and production; and project management, including printer selection and supervision.
To be a good freelance editor, you need to be well-educated and literate, and to have a good ear for language patterns, particularly for detecting the nuances of the writer's voice. You need to understand that the author-editor relationship is relational and not adversarial. There is a psychology involved between author and editor. I became an editor because I discovered that I am very good at helping others find their unique voice. I am a "midwife" of books.
Editors also need to be voracious readers themselves. Some of us are also writers in our own right. As Dick Margulis says, it is a calling more than a profession. I am a member of the Editors Association of Canada and of the Canadian Centre for Discourse and Writing (my academic side). I do compare notes with other editors, and wish there were a more systematic and supportive way of doing that. Too many editors operate out of competitive mode. I recently was helping with some editing for a company working with specific types of authors. This company had the editors peer-evaluating each other's work, an idea that seemed great at first. But I was dismayed to find that many of the editors saw "peer evaluation" as a way to tear each other's editing decisions apart. I would see comments on their bulletin board such as "I would never have advised the author to write x", or "If you knew anything about women, you would not have missed the author's point," etc.--in short, snarkiness posed as "evaluation." I personally did not receive any negative comments, but I was turned off by the process. So I'm not sure exactly how peer communication can work for editors, only that it needs to work better than it is.
The EAC is a really good organization and the editors are very supportive of each other. They have an excellent professional development program. In many ways, EAC's collegial approach could be a role model, far better than that other (unnameable) company.
The best exercise for anyone planning to edit — freelance or otherwise — is to write down all the "rules" of grammar and usage that you can find. When you think you're finished, do these three things:
First, read every grammar book ever written, noticing how much dissention there is among those "professors" who profess to know all those rules.
Second, read all the style manuals you can get your hands on.
Third, choose the style book you like the best (that one you agree with the most) and start to mark it up with your own preferences (derived from reading all those grammar books).
Once you have all this ingrained, ask your client what they prefer — and follow the yellow brick road. I kid you not; you have to immerse yourself in the vagaries of this crazy language, choose for yourself, and listen to your client. They call it "free" lance because we are blessed with a language in the U.S. that is ours alone — composed of every other language in the world. Embrace it, hate it, love it, and use it the best way you know how!