I left a position as a CAD technician to pursue my dreams of directing films and music videos (ah, the blissful ignorance of youth). So I enrolled on a film course that happened to have a graphic design module, though I'd never even thought about design as a career. My tutors noticed I had an eye for design and suggested I considered a design course at uni, which after a couple of years of working dead-end retail jobs to try and pay bills, I did.
That course set me up for where I am now, not only through the tutoring, but the access to industry contacts, opportunities to visit other countries and cities that I probably wouldn't have had otherwise (New York for example). There are many designers who are 'self-taught', and didn't study academically, though truth is much of what we do is self-taught. Nobody sits you down and says "here's how you design a logo", it's more about trial and error – you design something, get feedback, improve it, all the while training yourself to think critically about what you're doing and justifying why you're doing it.