One route is freelancing, using an online service such as Freelancer. However, I have to warn you that typically, if you don't have a record of success, then your freelance jobs will be really hard. You'll work many hours for essentially peanuts. But, the idea is that you establish a record of successes and happy customers that you can point to for future jobs. If you can live on essentially no pay for a year or so (either you have some other job, and programming is part-time, or you have a spouse who has a job, or you're living in your parents' basement, etc.), then this route might work.
Another route that also means very little or no pay for a certain length of time is to contribute to an open source project. Once again, the idea is to build a name for yourself and a record of accomplishments you can point to.
A third route is to show up where the software professionals are. You can actually go to a local company and ask to have lunch with a programmer or manager who works there. Just say that you're interested in the business and want to ask questions about the company. Not to beg for a job. You can also attend conferences and meetings for programmers, and schmooze. Talk to people about what they're working on, and get to know them. If nobody is currently hiring full-time positions, you could try making an offer to do something small for a limited duration, just to get your foot in the door.
Of course, you can do all three.
Unfortunately, if you've never had a programming job before, and you are self-taught, then the odds are very much against your getting a good-paying job right off the bat. Rather than being discouraged by the rejections, you need to accept them as par for the course. The most important thing you can do in the next 6 months to a year (or even longer) is to try to set yourself up as a known programmer, and not worry too much about the rejections.
Of course, this assumes that it is financially possible for you to go 6 to 12 months or more without a job. If that's not possible, then I don't know what to tell you.