People have making yogurt for 4,500 years. It is made by culturing milk with a bacteria called Lactobacillus Bulgaricus, which occurs naturally in Bulgaria. The bacteria eats the sugars in the milk leaving an acid which thickens the milk. People in warm climates make yogurt to help preserve their milk. There is a very long but cool article about yogurt at Wikipedia.
To make yogurt, we pasteurize two gallons of Flopsy's milk by heating it to 162 degrees on the stove. Then we cool it down quickly to 110 degrees by floating a plastic tub full of ice on top. We put one tablespoon of store-bought yogurt in each one of 8 super-clean quart-sized canning jars, add a little honey, and fill almost to the top with the warm milk. We put the jar lid on tightly. The yogurt needs to cook for 8 to 12 hours at a constant temperature of 110 degrees. There are lots of ways to do that. We found the quart jars fit in our old food dehydrator. We leave it on overnight, and it's done in the morning.