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Two books that I've seen mentioned other places are Audel Basic Machine Shop, which gives an overview on various machines, what they do, etc.
The next is basic blue print reading. Self explanatory.
An aptitude for math and geometry is certainly a plus as well.
I personally haven't used either but they have great reviews. I do use peter smid's cnc programming textbook in shop quite often. My dad used to let me mill on wood with dull tools when I was a kid to learn the basics and principals. Grooming me for the family business if you will lol.
As far as moving up, just show the imitative and a willingness to learn. Community college classes can teach you a lot. Our industry is experiencing growth as far as need, and guys in our age bracket aren't interested in the work. As someone said, learning the maitence on the machines is a good first step. Be vocal about your desire to become a machinist but be courteous too.