Sounds like you are already taking a class, so that's a good start. Does the school you're attending offer a class in basic machining? If so, jump on it, and take advantage of the Labs.
After that, it really just takes time. Start slow, be careful, and learn as you go. There are some simple projects you can start with; I made a nifty dead blow hammer about ten years ago that I still use to this day, and the project required me to do things with both a mill and a lathe.
I've been doing it for a dozen or so years. I literally started by drilling holes (thousands of them

) and have worked my way up from there. Today, I am a production manager at a small CNC shop that has three mills and two lathes, as well as the manual support equipment.
What do I do for fun when I get sick of CAD modeling, NC programming, writing quotes, etc?
I go out into the shop and machine me somthin' out of metal!
Takes the edge off, ya know?
Jim