One way to get an idea of the landscape would be to browse Java projects on Elance and Odesk. Not necessarily hire yourself there, but just get a sense of what people are contracting for.
Then maybe contact some business that use the kind of code you make, and ask if you can chat over coffee about whether and how they use contractors.
Doing those two things will give you some idea of the landscape. I'm sure there are contractors doing what you do – there are in almost all fields.
The easiest way to get started is to turn your current employers into clients. Talk to your boss about moving to freelance and tell them you'll be working from home. You'll have to make sure to keep your rate high enough (it will look higher than your current salary, but won't be).
Pitch well and they'll usually go for it as it's cheaper to have a contractor working than a full-time employee.
I've seen this done successfully multiple times, and never seen any employer turn it down.
* Save as much money as you possible can, and lower your expenses
* Start looking for a client or two on the side
* Think about what skills you can productize (e.g. an e-book guide to some sub speciality you're good at, in a niche who use that speciality to make money, and for which no good guide exists)
I'm interested in this second point. In your previous post you mention "Then maybe contact some business that use the kind of code you make, and ask if you can chat over coffee about whether and how they use contractors.". Sorry for being... naive about this, but I frankly don't know how this is done. Would you mind if I ask you a few more questions over email?
The gist is that people love to talk, and will rarely turn down a sincere request to give information. As I'm doing right now.
My brother got a job this way, and build a professional network at the same time. And almost everything I started in business came from a (well-targeted) cold email or phone call.
I think one of the most remote-work-friendly things a Java developer can do is develop Android apps. If you don't know Android it might be worth a look.
The problem is: I don't know what to do. Making webapps in PHP, creating web design, drawing, writing - I can imagine doing these things at home.
But I am a Java developer. Who would hire a freelancer to write a server-side code?
How to start?