How do you go about doing it? I'm in somewhat of a "transitionary" phase and have begun to start considering it. I think there are a few people on the board here that have gone about it successfully. Were there any books in particular that helped you out? Granted I doubt this is something that can really be covered in a book...
Wing it! Oh -- you want more detail than that.
Your biggest problem is going to be getting business. So, you need to advertise somehow. The best thing to do is to let everyone in your network know that you're going independent, and that you're available. Initially that's going to be everyone you've worked with whose name you can find. Later, it'll be every customer you've ever worked for (sometimes just sending out an email saying "I'm available" will spark something).
Your second biggest problem is knowing what to do with the business. Get yourself a lawyer, and for the first year or so go over every contract with the lawyer. If your lawyer is a good one, they'll go over each contract and tell you what it means. Somewhere on the IEEE site is a sample contract, that (IMHO) is something that I'd be willing to sign on either side.
If someone tries to give you some super-restrictive contract, don't sign. First, red-line the contract and send it back, with your explanation of why. Second, if they won't sign, just walk away -- signing a really badly written contract can leave you on the hook for far more money than you'll earn. Just don't go there.
Beyond that -- I don't do much firm-fixed price work, because if it's well-enough specified to bid firm-fixed, then unless you have a staff of low-paid beginning engineers, you won't make much money on it. Don't be shy about explaining that you'll only do a firm-fixed contract under the conditions that you get paid for doing what's in the specification, regardless of whether that's what the customer really wants, and that any change in the specification will change the price. Usually when I explain that the customer decides that maybe a cost+labor contract is better, even if it's less certain.
(Someone always loses out on firm-fixed: either I end up doing the work in a lot less time than I signed up for, or I end up taking a lot more. I can't refund when it takes less, because I need those projects to fund the over-runs. Such is life. If I had a huge staff I could level out the variations, but there's just me.)
That's the immediate concerns. Good luck, and remember that there's usually a path back to working for the man if it doesn't work out.
You might want to contact John Teel of predictabledesigns.com.
He has some experience in going solo.
I'm not affiliated in any way or form, just trying to help.
You will need to:
Define clearly the service or product and estimate competitive cost/price for it, competitive and differentiator analysis, i.e. business plan
Have a Marketing strategy and reaching out to your customers/clients, networking
A team to support or collaborate with you
Best of luck
If you think you're at a point where you might get some serious work, you probably should look into setting up an LLC as well, and asking around for a good accountant to help with either the LLC and/or taxes.