I started touring in college. I grew up in Colorado and did a fair amount of backpacking and camping growing up - so I had both experience and equipment from that. I went away to college in Boston, so a bike was one way of getting further away.
The first overnight tour was one I also organized for friends. The idea was simple enough, ride from Brookline, MA to the tip of Cape Cod and take the ferry back to Boston. Total distance was ~130 mile over two days and we didn't have definite camping reservations. My brakes didn't work fully, but that wasn't a big deal since I could sort of slow down and then put my feet down to stop

. About 10 miles in, I ran into a problem... The Claire Saltonstall bike route went through a park and the path went down a small hill and then around a bend. I went down the hill but missed the bend. As a result, my bike went off the path and stopped. I kept going and did a summersault over the handlebars and landed on my back. My backpack broke most of the fall, but there was a wound in my lower back where a sharp rock/stick had poked me. A reasonable thing to do would have been to turn back and get it taken care of... However, I was young, male and invincible. So my friends helped me find a place that sold a bandage. We bandaged it up and I continued. It still hurt a lot, particularly in the afternoon as sweat got into the wound and in the evening when my friends changed my dressing. As the day got late, we stopped by a church and asked if we could camp in the yard. That was fine as long as we were out in time for services. Not a problem and we cycled on to Provincetown the next day. It was triumphant riding into Boston after taking the ferry.
From that start, I did a lot of informal touring. This was particularly true starting summers after my sophomore year. I had a summer job with DEC in Marlboro that was 26 miles from Brookline. There was a vanpool, but I rode my bike ~60% of the time and took the van ~20% of the time. For the remaining 20% I would sleep out in the woods or in my cubicle. Some weekends, I would take off from Marlboro and head further outbound and hence I rode through a lot of New England. I was pretty gung ho and some days I could ride from sunrise to sunset and cover 150+ miles. I had a tube tent and would sleep beside the road at least as often as anything organized (or expensive). I did a few longer trips including ~1200 miles in a week from Boston/Montreal/Rivier du Loop/Bangor/Boston and many shorter overnight trips. I also led subsequent trips to the Cape Cod and Martha's Vineyard/Nantucket for my friends.
It was after college that I did more extended trips including my first coast to coast trip in 1992.
As far as questions you ask;
> Did you just decide to tour, pack up and leave one day?
Mostly informal college kid also riding overnight...
> Fully supported first tour?
No.
> Credit card tour?
No, but my camping equipment was also pretty minimal.
> Ease into by doing short trips?
Yes, sort of.
> Classes/experiences like ACA's Intro to Touring?
No.
> Jumped right into bikepacking?
No, I've ridden off road on a extended gravel roads and done more of what I think of expedition type touring (e.g. across Siberia, Argentina). I did parts of the GDMBR as well.
I do think how you approach touring can be different if you are younger vs. older.