You can make non-dairy yogurt in much the same way that you would make regular yogurt. You need the "milk", a live yogurt starter (this can be a yogurt culture pack you buy specifically to start your yogurt or you can purchase pre-made yogurt with
live bacteria in it). One more thing that I recommend, but that is not necessary, is a thickening agent (gelatin, agar agar) because non-dairy yogurts tend to be thin. Too much gelatin turns will make it more like Jello though, so if that is not your goal, experiment with smaller amounts first! (My kids actually like their yogurt jiggly, so I put extra gelatin in ours.)
I have actually written in length, with tips and pictures about how to make coconut milk yogurt here:
Coconut Milk Yogurt. The exact same process can be used to make soy yogurt. You can also see pics of my favorite way to make yogurt, cooler-filled-with-warm-water-and-left-overnight. By far the easiest way I have made yogurt so far.
I would suggest strongly that if your friend uses coconut milk, that the people who are going to consume the yogurt like the flavor of the coconut milk prior to turning it into yogurt. There is nothing like disliking the flavor of the coconut milk then making it into a more sour version of itself. It is not very pleasant to say the least. I would personally use fresh homemade coconut milk as that has the absolute best flavor by far in my opinion. It just takes much more time investment than if you were to just pop open a can or carton of the stuff from the grocery store. But it has the added benefit of not having stabilizers or preservatives added.
By the way, coconut milk beverage is not the same as coconut milk. It is like the difference between buying a jug of cow's milk and buying a carton of chocolate cow's milk. Coconut milk beverage generally has sugar, stabilizers and sometimes flavorings added, which is why it is labeled "coconut milk beverage" instead of just coconut milk.
Here is a link to some interesting findings by the WAPF on soy in general:
WAPF Soy Alert.