While you can use any plant-based milk, I have found that almond milk yogurt is too runny for my preference. You get something that looks more like a kefir when you use almond milk which may be fine for you. I don't use coconut milk because I am trying to avoid saturated fat. For me, soy milk produces a yogurt that I like.
Super Quick Version
My mother and I find it comes very close to dairy yogurt.
Take one packet of silken tofu and place in a blender. Add the juice of one to three lemons, depending on how sour you like your yogurt. Add 1/2 teaspoon salt and blend well.
Buy an electric yogurt maker. Pour soy milk into a large bowl and add your starter packet. You can also use unsweetened plant-based yogurt that you purchase from your grocery store as a starter. In my area, I have found that Silk makes an unsweetened almond milk yogurt that I use as my starter.
If you don't mind your yogurt a little watery then you do not have to boil anything ahead of time. Pour the mixture into the yogurt maker and let set for about 12 hours.
If you like your yogurt thicker then you should boil the soy milk and let it cool before adding the starter and placing it in the yogurt maker.
Check out the video. Once the yogurt has set, you can add fruit, etc
For Indians, who like their yogurt savory and spicy, I suggest squeezing some lemon juice to the finished yogurt.
Dr. Padma Garvey
The plant-based Doctor Mom