Add 1 cup of water to the coconut, squeezing and mixing the water and the coconut.
Using a strainer, strain this thick, first extract and set aside.
Next add the other 2 cups, do the same, and strain this thinner coconut milk.
When I am cooking curry (not Thai curries), I start cooking with the thinner coconut milk. Then, add the thicker one right at the end, for a fresher coconut milk flavour.
If I'm making dessert, the thicker coconut milk goes on after serving, as a drizzle/topping.