I'm 17. I chose not to do my senior year and instead got a job at a software company. From my experience, the number of people looking for young programmers far exceeds the number of programmers period (in major cities).
The best way I've found is to create a niche for yourself in software. Wether that's ops, node web development, ruby development, ios, etc. Create projects in that niche and post them to GitHub.com.
Then look for companies in your city hiring. Most major cities have tech job boards/mailing lists. Email the recruiter (or found if their email is listed) and let them know you're looking for work.
If it's a new company, even better, since they're likely trying to scale their system, offer to come in and see if you could help them get their API off the ground.
Most important note as your age is build casual business relationships with the tech scene, and you will get job offers regardless.
Don't work for free, don't take unpaid internships, you shouldn't have to do that, and it's not worth it.