Whenever people find out that I work from home and that I work through oDesk, their first question is always how I got hired. It's not an easy task, nor is it easy to explain. Let me give you more details why.
First of all, I got my first job on oDesk after months and months of applying. I went through tons of rejected applications due to the fact that I did not have any feedback on my profile, and I guess some clients just didn't like the thought of working with a newbie. So what did I do?
You should make sure to write a killer cover letter. State in your cover letter why you'd be a good fit for the job as well as any related experience you may have for the job, or any special skills you can put to use. It's also a good idea to attach samples of related work, or offer to create a sample, especially if you're applying for a writing job.
I think one of the things you have to keep in mind is that you should apply for jobs you actually like doing, as well as jobs you know you'll be good at. You shouldn't apply for writing jobs if you're not into writing, and so on. You'll want to build your online reputation and doing things you can and like doing is the best way to go.
Patience and perseverance also comes into play. You'll get rejected a lot of times, but then there's a chance that someone in the far side of the globe will take the risk and hire you. Once that person does hire you, make sure to give it your best so that they won't look for another contractor and keep giving you all of their projects.
That's pretty much all I can think of as of this time with regards to how you can get hired on oDesk. Feel free to leave a comment below in case you have any ideas or suggestions you'd like to share.