The basic recipe for vegan yoghurt isn't any different from the one for conventional yoghurt: add yoghurt cultures (from a store-bought yoghurt or yoghurt powder) to milk and keep warm for 8-10 hours. You'll find some tips and different methods in the notes section.
Put milk in a pan on the stove and heat until it reaches body temperature (about 105° F / 40° C). Check the temperature with your fingers/ back of your hand or by using a kitchen thermometer.
If using agar agar or homemade milk: bring milk to a boil (then add agar agar) and let cool to body temperature before proceeding.
Add yoghurt (or yoghurt powder) and pour milk into glas containers or the chosen container for the oven etc. (s. notes).
Depending on the method, either set the yoghurt maker to 108° F (42° C) and 8 hours or place in preheated oven/ underneath blanket etc. (s. notes).
After 8 hours, check for firmness and add thickening agent (guar- or carob gum, s. notes), if necessary. Now you can also add flavor like vanilla or sweeteners like maple syrup.
Serve right away or let set in the fridge for 1-2 hours.
Store in the fridge for 3-4 days.