You want the water to be hot, but not boiling. Add 1-1/2 cups hot water along with all of the coconut into a blender. Blend at high speed for 3 minutes.
Set a fine mesh strainer over a bowl or large glass measuring cup. Pour the blender contents into the strainer, and use a spoon or spatula to press the milk out of the pulp. This first pressing is coconut cream. (Alternatively, you can pour into a nut milk bag and squeeze the liquid from the pulp.)
Transfer the dry-pressed coconut pulp back into the blender and add the remaining 1 cup of hot water. Blend at high speed again, this time for 2 minutes.
Set the fine mesh strainer back over the bowl or large glass measuring cup. Pour the blender contents into the strainer and press the milk out of the pulp again. This second pressing is light coconut milk. Together, they make a beautiful full-fat coconut milk.
Refrigerate leftover milk. It will separate in the fridge, with the fat rising to the top. Simply heat it gently in a saucepan and stir it with a whisk to blend it into milk again. It will keep for 3 days in the fridge, or 3 months in the freezer.
If your local store only sells regularly shredded coconut, you can pulse it in your food processor to chop it up more finely.