@irontoenail - If you don't mind your frozen yogurt being quite hard then you can just make it yourself by mixing it up and then freezing it in the freezer. But most people want the soft texture of commercial frozen yogurt and for that you will need a machine. You could probably use an ice-cream maker if you have one of those, but the mix has to be agitated while it freezes or it will freeze into a solid block more like ice.
My friend who was in the boy scouts told me that they used to make ice cream by putting the milk and sugar into a can and then putting that into a bigger can with a layer of ice and rolling it around the yard for an hour until it froze. But most people aren't going to have the patience or time to do that.