1. Looks through a job listings site and copy and paste every interesting job into a text file.
2. Look for the commonalities and also the things you don't know yet.
3. Without lying, tailor your résumé to address the key commonalities you've found.
4. Apply to any and every job that you think you could do.
5. Create a mini-action plan for how you'll learn what you need to and put it into practice in order to address the skill and experience gaps you've identified.
I've found that when moving into a new industry three-six months of practice and examples are all you really need to get your foot in the door at least at an entry level.
Look for any and every way to use your current job as a place to showcase what you're capable of. Don't worry about getting paid more for it because you're investing in yourself and I guarantee it will pay off.
I got my first bit of programming experience working as customer service for AT&T Wireless. I learned web development, made them a couple of tools, got an award and then was able to find my first small time web development job.
edit: formatting