It's possible but very difficult to find a competent developer to partner with for equity. Especially if you haven't already established a good working relationship with developers through previous jobs. There's so many people in your situation lurking around tech meetups that it's become a bit of a stereotype. Try your best, but it's not easy.
Assuming you won't be able to find a developer to work for equity, you can make a certain amount of progress by hiring contractors. This is hard to get right, especially if you don't know anything about programming or at least writing a detailed specification. Unless you've got a large budget, in which case you should just skip looking for a founder and hire a pro to work as an employee, I'd recommend going the oDesk route, relying on the technical tests to initially evaluate candidates, and hiring multiple people simultaneously to do the same very small trivial task at first - until you determine which ones are good ones. There are some hidden gems out there, but you will waste a lot of time and money on garbage contractors until you find them. This is inevitable.
Your goal is, through your pocketbook and brute force, to get the product far enough along that it begins to generate decent revenue on its own (in which case you use it to hire), looks impressive enough to attract a little bit of angel investment (in which case you use it to hire), or looks impressive enough to persuade a developer to join you as co-founder. (Whether you hire or get a co-founder, the developer will then rewrite all the code your crap contractors put together.)
As inspiration, you may want to look at the recent Mixergy interview with Jason Jacobs, CEO of Runkeeper. I met Jason once, and he's an impressive example of a driven but non-technical founder who's managed to make a lot of progress. But be warned that you'll be doing a lot of pounding your head against the wall and the risk of failure is high.