Let a can of coconut milk sit in the fridge overnight, without disturbing it. Then open it, taking off the whole lid. You will find that the fatty part of the coconut milk—the coconut cream—has risen to the top. Scoop this off into a snap-top container. You can discard the watery part, or give it to the dog, water a plant, whatever.
Let the coconut cream soften at room temperature. Now whisk in a teaspoon of yogurt starter—or, for that matter, of yogurt; you can buy coconut yogurt at health food stores if you have to be really, strictly dairy-free. I have also pulled apart a probiotic capsule and used the contents as a starter, with good results. Just get some nice acidophilus and/or bifidus bacteria in there. Whisk the whole thing up thoroughly.
Put on the lid, and put your coconut cream in a warm place. A yogurt maker is ideal, if you have one. I line a mixing bowl with an old heating pad set on low, and settle the container down in it, then drape a tea towel across the top to hold in the heat. You could also put your container over a floor heat register, with a mixing bowl inverted over it to hold in the heat. Anyway, let your coconut cream incubate for 12 hours or so—I let mine sit overnight.