If you don't want to read my advice and just want my experience skip to the next section.
There's a reason contractors make more money; it's because it's a lot more work. The way I think of salaried employment is that it's an exchange. The salaried employee agrees to work for less than the market rate, and in exchange the employer agrees to subsidize your down time. In other words, you don't have to worry about constantly finding the next thing to do just to get paid. You get to focus on the work.
You'd be amazed how much work is involved contracting. You must go to networking events and startup meetups constantly for years in order to build up your identity. You must actually create your own portfolio website and keep it updated. You must keep your LinkedIn and Twitter profiles updated. You must do your taxes and send out W9s to each of your clients every year and follow up with them if they don't respond (and then talk with them more when they send you forms that don't match your records). You must meet with a lot of people and talk about their projects before figuring out that only 50% of them are even relevant to what you do, and of those maybe 50% actually get to the quote/estimate stage, and of those maybe 50% become paying contracts.
I'd say, when I was just contracting to support myself, maybe 50% of my time was billable; closer to 75% when I actually had a big contract that could keep me busy for a few months without worrying about lining something else up right away. So, if my billable rate was $100/hr, my effective rate was closer to $50-$75/hr. And then here in the US, taxes would take about 30%, so closer to $35-$45/hr.
On top of all that, you can never count on the work you have. You may have a need for X hours per week to sustain yourself, but that doesn't mean your clients will require X hours. They only need what they need. And being a contractor, what you need is officially not their problem. Of course, you could always work out deals with clients that guarantee X hours per week, but they'll only agree to it if they think they actually need more than that, and as soon as they stop needing it, they'll end the contract.
You could be living the high life with one awesome client, your bread and butter, for months or even years, and then suddenly wake up to an email saying they no longer need your services. Maybe the project they had you do is finished. Or they decided they were spending enough with you to justify a full-time employee to do it in-house. Or maybe the CEO of the company just found out his nephew does programming, and he can do it instead of you. Maybe their decision to cut you is a good decision for them. Or maybe it's a really bad decision that you can't prevent them from making. Doesn't matter. All that matters is that, as of this morning, you now have no paying work.
I could go on and on, as these are only the most pertinent warnings that come to mind. Hopefully I've sufficiently scared you. Cool. Now here's how I did it...
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First of all, I started contracting way before I needed to, just because it was fun, and it served as a way for me to get paid to learn how to do what I enjoyed and to become better. For years, I'd get up at 5 or 6am, go to work, come home around 5 or 6pm, make dinner, and work on my own projects until 2 or 3am. Having built your own projects is by far the best way to convince the first few clients to actually pay you (once you've done enough networking to meet them). I'd estimate I spent probably a couple thousand hours building my own projects, or building things in-kind for friends and family before getting someone to pay me straight up cash. I did this from the time I was a freshman in college to the time I was a senior (full-time student + job + side projects) before getting a paid contract I think, and then continued to do it for another year or so after college.
You may not have this problem if you're already salaried doing the same kind of work that you want to do contracting. I, however, was a mechanical and electrical engineer who wanted to build software. WIthout a relevant degree or official work experience, I had to teach myself and build stuff. After a few years building my own stuff, I also started doing a lot of open source work.
Eventually though, I had to start charging. This was hard. I started out, as anyone, low-balling some projects. Hopefully you only do that once or twice before you realize how unsustainable it is. Once I realized this, I started asking for more. I remember how guilty I felt at first, as I couldn't imagine that some site I could build would be work over $1,000 (!!!). It's actually funny to look back on it now, and realize how unsustainable even that was. I'm glad I listened to the advice or others at the time and didn't insist on such rates for long.
Like I said before, I continued to contract on the side, also spending tons of time grooming my own portfolio website, building side projects, working on open-source projects, and going to networking events (sometimes calling in my paid personal time to go to really good ones during the week), for several years.
I never considered quitting my job though until I knew I had enough work lined up to make the same amount I was currently making at my full-time engineering job. With student loans and whatnot, this wasn't really even an choice I could make. At times, it felt as though this would never happen. I couldn't conceive of a world where enough contract work existed that I could possibly line up. But I continued (I think this is where a love for what you do plays a strong role).
Eventually, through networking, I met someone who owned a web development company, and I discovered the world of sub-contracting. They had a lot of work and not enough people to do it. They wanted to hire me, but I knew I wanted to contract on my own. So we worked out a deal with me sub-contracting, and they could guarantee my at least 30 hours per week for the next 3 months. At our agreed upon rate, that was enough to beat what I was making as an engineer. I figured worst case was that I now had 3 months to find more work, and I put in my 2 week's notice. That was the scariest thing I had ever done (and in fact I wrote an article about it that became one of my first popular posts on HN at the time: http://www.alfajango.com/blog/if-youre-nervous-about-quittin...).
Once I was contracting full-time and setting my own schedule, I was able to kick my networking into high gear. Meanwhile, my new friend's company kept me on as a subcontractor beyond those few months. They actually ended up getting a big client that insisted after a couple months that I was the only one who could lead development of their project. Due to networking and word of mouth, I ended up getting a few clients of my own, one of which was big enough to sub-contract several developers myself. Thankfully by that time, I actually knew some developers who'd do it, developers whom I had met networking and working on open-source).
And the ball has been rolling ever since. I now own a company that builds startups full-time. We are a sort of CTO + dev team for hire; or a software-consultancy-meets-VC if you want to think about it that way.
It's much more awesome than my engineering job. So, I'm not saying don't set off on your own. Just that it's a lot of work, and that none of it is guaranteed to ever pay off. Right now, I'd say my team and I live comfortably, but it's still a lot of stress day-to-day. If I had taken all that time and effort that I spent to be able to contract on my own, and instead channeled it into getting a better job, I'd probably have a lot more money than I do now. But it wouldn't be what I wanted to be doing. That's the real reason to start contracting, for personal growth.
In other words, it takes a lot of work to build a lifestyle as a contractor. If you took all that effort and time, side projects and personal branding, and channeled it instead as leverage to find a better job, that'd probably be a much quicker path to making more money than contracting. So, I wouldn't contract for the money, I'd do it because it's what you feel like you must do to be happy.
EDIT: I should also note that, reading through some of the other comments that say "it's as simple as getting a client, going to meetups, etc." I was tempted to say that at first too. I sometimes forget how much time I spent going to meetups and building experience before any of this really started becoming "simple" for me. It's easy to look back on the past 9 years I've been doing this and forget how much work went into each actual year, or how long a year really is.