I have made yogurt on the stovetop numerous times. I followed the recipe in the NY Times from several years back. Basically, you get out your biggest pot, fill it with fresh milk (the fresher the better -- shouldn't be longlife) and heat it, checking with a candy thermometer. You have to add existing yogurt (for the culture) but I think you do this after you take it off the heat. For it to set, when it cools a bit (going by the thermometer) you put it in the containers you are using and they have to be kept warm for a certain amount of time. (BTW, this is all a yogurtmaker does.) I used to put mine in glass jars and put them all together, wrapping the whole bunch in a large blanket and leaving it overnight. Some people put it in a slightly warmed oven with the light on.
As I understand it, "Greek" yogurt is strained. I have done this as well -- you just wind up with a lot less yogurt, but it is thicker.
I have just described the process but obviously these aren't directions -- I don't remember times and temperatures.
I did this a few times and felt quite virtuous but stopped because I always did large amounts and then had trouble getting it all in the fridge, it was not necessarily better than what you can buy at the store, and I didn't think it worked out to be meaningfully less expensive.
It was a fun thing to try but there are other things you can do at home where there's a bigger difference compared to store-bought and the effort is more worthwhile. (Bread, cakes come to mind.)