Start with warmed milk, I prefer whole milk (but I don't need it). You can use very little culture to start, sometimes I've just swirled the milk around in an empty yogurt container (always plain live yogurt, never flavored or sweetened), but most folks start with about a teaspoon to a tablespoon.
Place in a non-metal bowl, the heavier the better (I have an old ceramic bowl that I like best), and then start warming the milk in 30 second bursts. Don't stir, just use 30 seconds, then let it sit for 5mins or so. You can certainly temp test, but I don't, I just feel the bowl. You want it no warmer than what you'd feed a baby. It needs to stay warm like this for a few hours, 4 is a minimum for me and 8 is a maximum, and then you either simply refrigerate, or strain through muslin (cheesecloth isn't fine enough), et voila, Greek yogurt.
If you're worried that something else might be able to outcompete the yogurt cultures, then cover with plastic film. I've yet to have something else grow.
The higher the fat content the nuttier and less tart the flavor.