I use Elance and it is a great way to earn money - I like a couple of others on here work as a freelance writer full time. The best way to get started is to do one or two jobs at a low rate - if your level of English is good you will easily find someone to take you on. Once you have some good feedback other employers will also be happy to work with you and be willing to pay higher rates.
I generally ask for $10 an article (500 words) on there, and there are a lot of people who are willing to pay this. One employer (Sienna Miller's hairstylist apparently) paid me $50 for a 500 word article - that's my best so far.
When applying for a job, most people will ask for samples. It is not a bad idea to link to your HubPages profile as well as sending over a couple of articles that show your best work. If your articles are related to the subject the employer wants - even better.
Aside from this you need to show each employer that you have read their instructions. Don't send the same generic email to ten people and expect it to work. If an employer asks specific questions, take the time to answer them.
You can also sign up for a paid subscription on the site - this will give you more credits and enable you to apply for more jobs.
I also run my own personal writing site - http://www.inkelves.com which I send to my employers. This also shows a level of professionalism I think. As soon as you get your foot in the door on those sites though you are on your way. That is the hardest part yet it can be done.
Hope this helps some people!