Qualifications
Quick—stop registering for classes. You're not one of those roller-chair jockeys in an office who wouldn't know a lathe from a mill. To make it in the world of machinery, all you really need is training. Sure, you'll need a little, tiny bit of formal education: a high school diploma, replete with some demonstrated coursework in trig and geometry.
If you want to go the extra mile to get an additional step up over your competitors, there are post-secondary options. You can get a certificate in a specialty like benchwork, drafting, or computer-controlled machines (source). You can also keep the mental gears turning with an associate's degree at a two-year technical college, where you'll learn your way around blueprints and computer aided drafting (CAD) in no time.
Once you feel you've got the skills you need, get a certificate from the National Institute for Metalworking Skills. Then you can head out into the world and take whatever apprenticeship you can find. You'll need to squeeze everything you can out of the apprenticeship because there's a lot to learn, including computer skills like CNC machine tools, CAD/CAM programming, and so on. Didn't love your Computer Programming class in high school? Learn to love it.