In addition to things that were said, I found some good work on Elance.com, and small projects then evolved to things that kept me busy full-time.
For me it was a bit intimidating to begin with since I had to compete against developers whose bids were a fraction of the price I quoted. However, I soon found out that there are still people out there who value quality and are willing to pay more for it, so the "secret" is to make sure you put a quality bid. What worked for me was:
1. Make sure that your offer refers to the project description. Even highlight issues you find. There are lots of people out there who don't read the details and so people offering work appreciate it when someone actually read and thought about their project.
2. Describe how the project relates to an experience you have. Show a couple of examples work you have done with similar nature.
3. Include a sample of your work. In a couple of projects I was told that I was the only person who did that. I won both contracts although I had the most expensive bid.
4. Be responsive if the customer is asking questions before they make the decisions. Despite not winning all those projects where I had contact with the customer, it gave me an insight to their thought process, and even when I didn't win, it was useful to know I was a runner-up (and where possible, why I didn't win the contract).
5. Don't under-price yourself. There are probably cheaper developers than you, but are they as experienced as you are?
6. Don't over-price yourself. There are some naive customers who estimate a work to be more expensive than you think it should be (yes, really). It's tempting to be greedy and up your price, but I found out that being fair led to long-term relationships and to people who kept me so busy I didn't have to look for new clients for a while.
Hope this helps.
Edit: formatting.