So, I took a medieval bread class once upon a time. There's a couple of things going on here. To understand yeast bread, you have to go back to beer. Beer was kinda and accident, and from my limited understanding can cultivate wild yeasts for fermentation.

Anyway, people had beer for centuries before they decided to get to bread. Most bread in the middle ages, especially for poor people (read most people), is nothing like we know of bread now. It was not leavened (read no yeast) except for some cases of steam or vinegar leavening. Mostly bread was a flatish, dense substance. Most similar modern mirror is a bannock, but most people wouldn't have wasted the milk, egg, or butter on bread. They were too poor for that. Bread also was not wheat for most people. Pea flour, oat, rye, spelt, and occasionally when were used (that I know of for northern Europe from about the 6th century to the 14th. After that I'm not sure).

However, yeast breads did exist. Only wealthy people had the means to make it though. Notwithstanding the yeast, you need an oven to make it, which is an expensive and time consuming thing to make and use. Maybe a whole village might share one, but most often only wealthy people have one. Then, you need glutenous flour. Wheat, rye, etc was really only available to wealthy people.

Once you have all these components though, the yeast is rather simple. Beer. Most yeast breads start with a starter, like sourdough. To make this starter, you skim the beer, mix it with flour, and wait. It will start to bubble. Then, you use most of it for your bread, feed the leftover more flour, and set it aside for the next day. Over time, the starter will collect more wild yeast from the environment around it, and keep a nice little culture going. If you get a good colony of yeast going and keep feeding it and using it, mold generally isn't a problem. This also wouldn't have tasted like a sourdough that we know today. Unless you let the starter actually ferment and start to produce alcohol, it will taste like normal-ish bread. Quite good actually.

As to how someone thought to put beer in bread, no one is quite sure (that I'm aware of) why they tried it. I chalk it up to a good old human "hold my beer" moment. But the end result was a fluffy bread that became a symbol of wealth.

Edit: sorry, for clarification, the active dry yeast we know was not a thing. People also didn't know what yeast was. They just knew that if you left beer long enough it would bubble and make alcohol, and similarly a bread starter would do the same. The beer foam was often called "a gift from God".