Networking is the primary way to find and win work. Elance/Odesk and the sorts are worse than useless for a US based person as they are all a race to the bottom. Also, you will find that the clients that pay you the least are the biggest pain.
Everything you can do to build yourself up in the community helps. Writing a blog, putting yourself out there, contributing to open source projects etc all count a lot. But nothing beats talking to people and winning their trust because then they will turn to you and give you a shot on a project. If you can make yourself a niche where people seek you out for knowledge over some specific in demand tech that is awesome. But that usually takes more time then getting out and meeting people to get work. So you should do both, but just recognize one has quicker payoffs than the other, usually.
When you are starting out stay away from RFP's, the process and overhead to properly answer RFP's takes more than you can afford when starting. A lesson I learned the hard way early in my consulting.
Also, find a consulting firm that needs some additional help and contract to them a few times on their client projects. A lot of times this is a way to broaden your network and your skills to find your own work. Plus you can see how they are doing things and then take what's good and replicate or improve on it.
2. Share that something on your website/blog etc
3. Write about your work, what you are doing, how you are doing it etc.
4. Go to local meetups, find people in businesses who have problems and try to offer them to solve it for them. Do this offline in person if possible.
5. Write more online about your stuff.
6. Be part of open source community and try to make contributions to projects that interest you.
Pro tip: Odesk/Elance etc are great if you want to compete with low cost programmers from all over the world and there is a reason for it. You are not really showing anything special to a prospective client other than your "portfolio" which is very similar to most other freelancers on those sites. Of course, there are some gems to find but very rare. Any good freelancer will have their own setup, own website, own blog, own showcase etc. Again, it takes time to do this.
This takes effort but doing this will increase your chances significantly.There is no magic wand to this really. The best freelancers/contractors are those who do most of the above steps on a regular basis. It takes effort to show you want know AND build a reputation for how good you are. But people will never know unless you show them.
I will give you an example. Whenever I am searching for a technical issue on google and if I come across someone's blog/github explaining those issues, I immediately have them in mind as potential freelancers who could help me in future. Doesn't matter if they are in NY or Maldives.
I haven't looked for work in about 2 years. I'm lucky enough to get referrals these days.
In many contexts "consultant" is somebody who has specialist knowledge in some area and is able to advise / guide the client to accomplish a desired outcome.
A contractor, on the other hand, is somebody with a specific skill-set who undertakes to produce and deliver some deliverable to the client's specification / requirements.
Unless you are already known for in demand skills, you need to prospect for work. Yes, it is selling and many of the other comments here have great suggestions on how to do the marketing.
In my experience, you need to work in a job to build up your skills, experience and contacts. Without that background you are probably only going to get small jobs and take a long time to build up your profile to be demand for the better paying gigs.
My experience with elance/odesk is pretty terrible. Focus on quality not quantity clients (even in the early days).
Nothing wrong with taking a full time job and doing said contracts on the side either - so long as the client understands, of course. And once you've built a portfolio app/site on the side then they'll have some degree of confidence in your ability to deliver.
Good luck.