I have not done anything CAD related for my career since late 2010. I've continued to draw/design stuff for my own use, but all of my software is pretty out of date at this point.
My training was initially formal, but I took that and kind of ran with it, teaching myself other CAD software as time went buy.
Probably more details than you want to know, but here's my story:
I was perusing an engineering degree, I eventually changed majors, but while in the engineering program some of my required classes were design classes. I took a drafting course, where during the lecture, it was hands on, pencils, rulers, compasses, protractors, and graph paper. The lab for that class was computer drafting, on AutoCAD 2000, which was 2 or 3 years old at that time, depending on when it was released.
I hated going to the computer lab, I had a computer in my room, at my house, and as a student I could buy AutoCAD 2002 LT (student version) for about the same price as one of my science books, so I bought AutoCAD, and did most of my work from my own computer.
I was fairly big into car audio at the time, and wound up designing a bunch of speaker and sub boxes for folks. I naively shared one of my designs with a car audio shop in TX, I thought I was helping some guy out, not doing free design work for a shop, but I digress.
My continued use of AutoCAD for various projects, for years after that, got me a "consulting" job, right out of grad school. There weren't a lot of folks hiring at the time, and drafting didn't have anything to do with my environmental science degree, but a good friend that worked for Air Gas had a customer that was starting up a boutique trailer and fab shop. These guys had previously just done paper sketch designs, and farmed out all of the fab to other local businesses, but were in the process of vertically integrating to do it all themselves. They were all fairly computer illiterate, let alone CAD, and my buddy told them, "hey I know a guy."
I went to work for them as a part time consultant, originally just taking all of their current products and designs that they'd been having built for years, measuring them, and drawing them in CAD.
They were sold a BobCAD suite before I came onboard, which at the time, was garbage. I don't know if BobCAD has improved since then, it may be the best thing since sliced bread now, but my experience trying to use it, and their customer support, got me to swear it off. Avoid it like the plague. To avoid my frustration with BobCAD, I took to using my own, at this point, very old version of AutoCAD at home. I was basically drawing and measuring everything on paper, going home and drawing it on AutoCAD.
I'd take the files I drew on AutoCAD, and import them to BobCAD, since they also used BobCAM for their CNC plasma cutter. I taught myself g-code, and got a crash corse in CNC operation from one of the Air Gas "gurus."
I knew if I was going to do more than consult for these folks, I needed a better solution than my ancient AutoCAD, that couldn't render 3D models.
I "acquired" a, um, Russian maybe?, copy of Solid Works '07, went through the tutorials, bought a couple of books, and taught myself Solid Works. It was really intuitive, especially with already having some drafting experience. Learning weldments and assemblies were really the only "new" concepts.
After seeing their products in pretty 3D Solid Works renders that I'd drawn, they were convinced to hire me full time, and buy Solid Works.
I worked for those guys for about 3 years, soon after going to work full time, I was designing new stuff, not just measuring and drawing old stuff. I did all of their drafting, created all of their blue prints, and ran their CNC plasma table. I did that, all from just having only taken the one drafting class many years prior.
I sometimes miss the challenge, and seeing things I designed become a reality, but that's not where my passion is. I'm happily making use of my degree now.