It might sound trite, but in many industries, it really is all about who you know. It's a lot easier to get an interview if someone within the company vouches for you, so get out there and meet people in your desired field. Scope out some local business networking events, grab your business cards, and start schmoozing. You can also set up an informational interview, where you chat with someone in the industry to get a feel for what you need to know. You'll gain valuable insight into your new career path, and, if you're lucky, you might even get yourself a job offer out of it.
If your dream job involves working for yourself, networking is just as important. You need to build up that client base so you can afford to keep the lights on. It's also helpful to build up a support system of other local entrepreneurs, so that you have a network of people who you can bounce ideas off of or ask for help when you're stuck.