Sometimes, companies who don't advertise remote positions are willing to try it. Sometimes, companies who prefer full time salaried employees are willing to bring you on as a contractor. Sometimes they may even be willing to consider a short 3-6 month gig to build out a prototype or project that they'd been meaning to get to but never had a full-time dev to throw at.
The only way to find out is to ask. Good developers are hard to find, and good companies know to grab ahold with both hands when they find one. If that developer just happens to want to do his thing remotely, in short bursts, or even from the beach in Costa Rica, that might not be as much of a stumbling block as you think.
You're going to have to do sales of some kind. Outbound is faster.
Proactively talk to people who need professional services, talk to them, understand their needs, explain their business to them and then tell them that you can do it, for X. X is a lump sum or a number of hours billed at Y, doesn't matter. Sell your business and be on point.
Do not be the guy who does "oh this takes X hours" and then it takes 3x as many hours.
Be professional. And don't mind anyone else. Don't compete on price. Compete on quality.
If you can't do the outbound sales thing, apply to Toptal and Gigster. On toptal, its the same thing. People say you can't earn a decent rate, which is not true. I showed up there, with my very lofty rate, and made it happen in a week. Exactly the contract that I wanted. I'm working part-time on a full-time salary that dwarfs anything I could make anywhere in the world outside of the Valley while living the good life.
Just be quality. It's 2016. If you're good and you can make this your profession, you'll live pretty well.
And pay the naysayers no mind. There is no race to the bottom. Indians who charge $15/hour are just fundamentally bad. The really good indians won't work for that rate either. They know what they're worth. Compete on quality.
It is fundamentally impossible for there to be a race to the bottom, since there is too much demand. If anything, we are experiencing a race to the top and its only begun. Increase your hourly by 50% per semester at least until you hit $250/hour.
It started out small. With only a handful of small jobs, but if you make your clients happy, more work will come.
The more established you become, the more access you will have to higher paying clients.
I'm fairly new to using it myself, and while I've not gotten any work through it so far, I have gotten a couple phone interviews, so it's not nothing.
Even though most clients there want to find cheap labor, there are some that understand they need real expertise and are willing to pay for it. Not sure if you find it worth the effort to dig through the crap projects.