I was first introduced to making yogurt by my aunt and my sister-in-law. At first I thought it sounded disgusting, like the yogurt would be bad because it was left "out" too long. But that's what makes yogurt. You need warmth for the culture to grow.
So, here is a link to where I went when I started making yogurt: Crock Pot Yogurt. Follow the directions exactly at first and then tweak it and experiment with it as you like. It turns out great! I use a strainer rested on top of a deep bowl with a extra large coffee filter in it. Fill the coffee filter with homemade yogurt, which will be thin, and strain overnight. In the morning you will have thick yogurt.
I have recently started making yogurt out of part cow's milk, part soy milk and plan to try coconut milk soon. Hopefully this will help my son with dairy sensitivity.