Whirl ingredients in a blender for a bit. Then dump that mess through a strainer lined with two layers of cheesecloth.
Let as much liquid drain out as possible. Gather up the cheesecloth and start squeezing to get all the liquid out you can. You can adjust the thickness by using more or less water.
You can get a second "pressing" out of the coconut shreds, but that will be much thinner milk.
Fresh coconut or unsweetened dried coconut can be used.
Coconut: Although classified by the FDA as a tree nut, coconut is not a common allergen and is not related to tree nuts. If you have a tree nut allergy, consult your physician to find out if you need to avoid coconut.