Heat the milk to 180–185°F (82–85°C) in a pot, stirring now and then. No thermometer: very hot and steaming, but not boiling. If you're using ultra-pasteurized milk you can skip this step and go straight to the next one.
Let the milk cool to 108–113°F (42–45°C). If a skin has formed on top, lift it off. No thermometer: like warm bath water.
Whisk the yogurt with a little of the warm milk in a separate bowl until smooth and lump-free. Then stir it into the pot.
Cover the pot, wrap it in a towel or blanket and let it ferment in a warm spot for 6 to 10 hours, undisturbed. An oven turned off with the light on works perfectly.
Once it has set, refrigerate for at least 4 hours. This is where it finishes firming up.
Set aside 40 g in a small jar to use as the starter for your next batch.
To make it Greek style (optional): strain it in the fridge using a strainer lined with cheesecloth. 1 to 2 hours gives you a very creamy yogurt; 3 to 5 hours, considerably thicker.