In terms of choosing the right service provider for your project, there are a variety of options on Elance and each situation is unique.  There are a few general strategies and tools on Elance that can help finding the right match easier.

Is time of the essence?
If you need to get something done faster, it may be safer to go with a more established provider who has done several projects that have received good feedback ratings.  Experience with the Elance system and a track record of reliable performance is a good recipe for future success.  Most of the service providers that have been on Elance for a while are proud of their work and reputation on Elance and exhibit a high level of professionalism.

Do you want to get the best price?
You can get exceptional value all across Elance, but if you are looking for some of the best discounts out there and you aren't under strict timelines, you might want to take a chance on a new service provider or two.  There are many rising stars that are eager to prove themselves and willing to work for less to build their Elance ratings.

How much help do you need defining your project?
If you need help defining parts of your project or fleshing out ideas, communication and local knowledge should be factored into your decision.  Native English skills and experience with local markets and business practices can be considerably valuable in such cases.  Conversely, if you know exactly what you want and what it requires to get done, leveraging skill sets around the world may be to your advantage.

Who is the right match for your project?
One of the best indicators of success for projects is whether the service provider has experience that matches your project requirements.  On Elance you can see provider profiles (like a resume), the projects they have worked on, and the feedback they have received.  Reviewing their portfolio and way they present themselves are also helpful for determining if there is a match in terms of style or personality.  If you like, you can even ask the providers for references that you can call.

Who shows the right initiative?
Look for providers that show that they have taken the time to understand your project when they make their bid.  In the initial message that you receive when someone places a bid, clarifying questions and references to specifics of your project are better indicators that they understand your project needs than generic messages that just list their general qualifications.

Clarify and learn
The bidder selection process can be as interactive as you like.  You are free to communicate with providers using the Elance private message board to clarify bids, negotiate agreements, "interview" applicants, or whatever you might need to make the right decision.

Narrowing down the options
It is good to get a variety of bids to choose from, and Elance has some features to help you manage the selection process.  Shortlist bids to focus on a few bids without limiting your other options.  Decline bids from providers you are sure are not qualified or you are not going to choose.  You can also award the project at anytime or close the bidding early if you have received enough bids to review.  You don't need to wait until the bidding closes, since most of the bids should come in the first few days anyways.

Getting more options
If you aren't getting enough bids or the right skill set matches for your project within a few days of the project being posted, you might want to consider inviting a service provider to bid on your project.  This strategy can be especially effective if your project requires experience or skill sets that are more unique.  There are providers that may have the exact experience you need that may only know to bid or be able to bid if you invite them.
Here is how to invite a provider.

Offers to go outside the system
During the bidding process, there may be an occasion where a service provider offers a lower price if you go outside the Elance system.  If such an incident occurs, we ask that you report it to Elance.  Working outside the Elance system opens you up to more risk, as the provider does not need to worry about an Elance feedback score and Elance cannot help you if things go wrong or with payments.  In addition, this type of behavior is strictly against the Elance terms of service, and is not fair to other members of the Elance community.