You can get clients from oDesk or Elance, and easily. But...
1) You have to differentiate yourself. You can't look like 100s of other providers, your description must be in some way unique and you must looks like a REAL deal (and better be a real deal, otherwise market will quickly sort you out... or you will have a hard time delivering services...)
2) NEVER ever go for a cheap jobs, and never ever go for hourly paid jobs (unless you have in mind a plan to convert that client into Escrow job later on, or you have feeling he is a good source for a future...).
3) Pay a monthly fee to Elance, that enable option to see other provider offers, plus will give you some other options.
4) If you see bunch of guys offering "services" for $100, you go and submit one for $1000 (if you can read between the lines of proposal...) ... or
5) ...BETTER, don't give any amount at the first step. Just submit proposal, ask a lot of questions and gather intel (that way you can quickly screen out PITA clients, and adjust your offer to the needs of client. Also, it will give you some time to rethink your proposal, and if you are actually a good guy for the job).
6) Often marketplace is "dominated" by some sort of services or providers that clients are not happy with. All of these have some serious flows. You can use that flows to your advantage, so you can show clients that you are different and you understand their pain. For example, many guys out there that provides "SEO" services, gives clients promises of all sorts, and often on a freaky low budget! Many clients go for it because they want to "save" so money. But once they get fucked, they are more open to reasonable talk about business.
7) Be as personal and yourself as you can. Sure, keep the story about your SEM agency (if you have one) ready to use, and use it in a right time. But for gods sake (I'm atheist BTW..), don't put that stupid small logo of yours as a profile image... unless! You want to work with a bunch of low shelf, PITA clients.
8) Go for Elance. oDesk is dominated by cheap bitches. Sure, you still can get a decent clients (my friend get one paying $900/M for really stupid things..), but still Elance can provide better opportunities if you really know what you are doing.
I have started with Elance and oDesk. Elance quickly became for me the best source of clients. From a bunch of those, I have two GREAT ones. So, as for starters without better idea I would say Elance could be a way to go. Once you have delivered a good job to the good clients (that is important!) you are ready to go. Because good clients are the people who have friends, and their friends also have friends... and so on.
BUT!!! (That's critically important!)
You have to make sure you are getting into the right pound. You want good clients, not PITA clients. Just imagine, what will happen when you get a good looking PITA clients and he will start sending you his PITA friends... you don't wan't this to happen.
Elance is a good place to find a good clients. I know many people from this board will not agree with this, but still... it's true. And, it gives some sort of "training" for a bigger fish.