Furthering this meaningless question, basically we get in touch with a programmer, personally, and we send him informal requirement descriptions, (not contracts) and when he sends back working code we pay him via credit card/online.
Trust? When he sees that we do pay him, he'll do more jobs. This is not an employment model for millions, so please leave the legal issues.
You can use
Elance is more structured and you find genuine bids.
With all due respect, only a complete idiot would do work with an unknown client under those circumstances, unless the project is trivial and the developer desperate. Putting aside the trust issues, the most important part of a contract for me as a developer is the limitation of liability provisions.
prashant_sp mentions some sites that work the way you want. But keep in mind that you are entering into a contract with the site you use (even if it is hidden behind a TOS page), and you'll have to pay the developer even if you are not 100% satified. Also, most good developers will demand some cash upfront.
First of all I strongly disagree with MadCoder's oppinions. I, for example, frequently work with RentACoder.com :
First contact is made on the site and I release the first software for a buyer using RAC as middleman (thus trust issues are no problem due to RAC middleman nature). After this first contact, I am sometimes contacted privately by the buyer and agree to another project, exaclty how you described it in your question. Because a trust relationship is settled on the first project we now have the advantage of eliminating the middleman with it's commisions.
To summarize, I recomend you to try one of the many frelancing sites you got here (I only know about rentAcoder.com and am very pleased with it's services) and try to create a connection with one or more coders on a test or small real project. After that you can continue with the coders privately.
Ohye... RAC is last choice in your view ...but I like it more , I use oDesk but that is trouble to me , I do not know why , others still no experience , I will try elence soon.