As vaccines go, this was pretty crude (and icky!)--dip needles into "ripe" smallpox sores, and stick these pus-dipped needles into a small incision on the arm of the person to be innoculated, then cover the sore up with a nutshell and pray. Within a week, if all went well, you get a very very mild case of smallpox, with lesions that don't leave scars, low-grade fever only, and then you're immune for the rest of your life.
Icky, yes. However, the point to be stressed is that this was the first real vaccine, even as crude and nasty as it was--and nobody'll ever know who invented it, or how. It was practiced largely by women (ostenibly in fear of the ugly scars of smallpox as much as the 1-in-3 mortality rate, although I submit that this is the worst sort of nonsense) and was considered primitive oriental superstition by the intelligensia at the time. These were illiterate women--they left no writings, if they had an oral tradition it's completely lost, and we'd never have heard of this at all if not for this French woman who happened to be in Turkey and had a personal interest in smallpox (having survived it herself.) Nobody who was anybody thought it actually worked, and it was only decades later that the scientist Edward Jenner created the modern smallpox vaccine, made of cowpox and, like all scientists, building on the research of those before him.
So we'll never know who really invented the smallpox vaccine in its first form. It was probably a woman, given the cultural spread, who somehow, in the absence of even the faintest theory of germs, figured out that old smallpox sores were the key. Unsung genius? Maybe. Crazy dumb luck and serendipity? Most likely--luck lies behind many great scientific advances. Still, someone had to observe what happened and draw a connection.
History is full of weird little stories that we'll never know the answers to. But hey, it keeps the historical fiction writers in business.