People have been baking leavened bread (the kind that rises) for thousands of years—long before yeast was commercially available at the local grocer.
Yeasts are single-celled microorganisms that are classified as fungi; there are more than 1500 different species and they are everywhere! While a few of these are not our friends, many more are: they help us make wine, beer, vodka and all sorts of baked goods.
You can have fun (and give kids a science lesson as well http://robdunnlab.com/projects/science-of-sourdough/) collecting and growing your own “wild” yeast.
For single-celled organisms, “growth” mostly means reproduction, turning a few individuals into many and producing a “culture” or “starter” than can be maintained almost indefinitely (some record-holding starters are over a hundred years old). Yeast can be attracted and grown using all kinds of foods, from wheat to potatoes to fruit; and the species of yeast you collect (and the friendly or unfriendly bacteria that join them in your culture) vary with where you live, and what you collect them on, among many other things.
Here are a few links to get you started collecting your own yeast!