These are the things you will need:
Soy Milk; A small cup of store bought soy yogurt with live cultures to use as a starter (any flavor); a spoon of sugar
A measuring cup; A pot; A cooking thermometer; A wide mouth thermos
Boil water and pour it in your wide mouth thermos, let it sit. This is to sterilize the thermos. Also pour boiling water over the lid.
Pour the amount of soy milk necessary to fill your thermos into the sauce pan. In my case this is about 2 cups. Heat the soy milk, stirring occasionally, until it reaches a temperature of 160 to 180, but not exceeding 180 (Do not boil). Turn the stove off and remove the pot from that burner. When the soy milk reaches a temperature of between 120 and 115, but not exceeding or falling below that, stir in a spoonful of sugar (to feed the yogurt culture) followed by about 2 tablespoons or two heaping spoonfuls of the store-bought yogurt (this is correct for adding to 2 cups soy milk). Stir it well. Pour the water out of the waiting thermos and pour your yogurt mixture into the thermos. Place the lid on the thermos and set it aside for 10 to 12 hours. Do not move or shake the yogurt during this incubation period. After this time has passed open the thermos, stir, and pour into a container to place in the refrigerator. In subsequent yogurt making you may use your own yogurt as your starter. I have done this for about six generations with each batch turning out fine.
The soy yogurt should have a good consistency but be a little runnier than most brands purchased in a store. If you attempt to use nut or rice milk the culture will take but it will likely stay very liquid. My first attempt at yogurt making was with almond milk and the result was a yogurt tasting almond milk. However this was also before I started adding in a spoonful of sugar and using a wide mouth thermos to keep the temperature steady during incubation.
I was interested in how to make a yogurt starter without having yogurt in the first place. I have not tried this but it is my understanding that you can make a yogurt starter using five chili pepper stems and a dried tamarind, Using this in place of the yogurt starter to make the first batch.