I taught myself to program and got my first programming job during the dot com bust. I've since become a manager and have done a lot of hiring so I can speak to both sides.

First, don't worry about not being as good as "us". Most likely we're not applying to the same job as you, and most likely we're not looking for a job at all. Most resumes I get, and interviewees I interview are absolutely awful. The bar really isn't very high, you just have to get to the phone screen.

So how do you do that? Build something real and be able to talk about it. You need to be able to point to something and say "I made that". It can be open source or it can be your own website, a free mac app, iphone game, whatever. Then, focus your applications to job postings that align with your skills and background, and write a cover letter about the thing you built. The cover letter will help the reviewer overcome the lack of experience on your resume. Most job postings ask for someone with n years of experience. Ignore that, just ensure that they are looking for a junior person so you don't apply when they are really looking for a senior person.

Focus on smaller companies. Big companies have HR departments that review resumes and they primarily look for x years of experience with J2EE blah blah blah.

Be willing to take less money than someone with experience if all else fails. There are a ton of people out there that want to hire a programmer, but don't want to pay $70k for a junior developer. If all else fails, go to one of these places and make 40k or whatever, and within a year you'll have job experience on your resume and you can easily get a new job for more money.