Go to meetups related to whatever stack you are into. It isn't uncommon for people who have small companies to pull employees directly from those communities. I've seen posts go out to the meetup lists that specifically state that they would take new and inexperienced devs. The flip side, I imagine, is that the money isn't going to be great, but you'd hopefully be getting a lot of mentoring.

Also, a lot of people will say "write code," and that is absolutely true. Get stuff up on Github that you can show off. That will show employers that you can actually code.