We never "officially" learned to draw blood in nursing school, but in a post-clinical our instructor reviewed some of the basics of it with us. He said we'd probably have to do it some day, and he was right!
For the most part, however, I learned by following a phlebotomist at the hospital I was working at and performing 20 draws of my own. Our facility had changed its policy in that 7p-7a nurses were to begin drawing a.m. labs, so the training was required on that basis.
Since that time, I've had several jobs where drawing blood was a necessary skill (Dr. offices, home health). It's actually one of my favorite skills now, though in my current job I don't have to do it.