Use 1 cup boiling water for each cup of tightly packed fresh coconut pulp. Mix boiling water and coconut. Let sit for at least 15 minutes (30 minutes is better). Place mixture in a blender, and blend for 1 minute (this helps to extract even more coconut milk). Strain the coconut milk from the solids using cheese cloth; you won't be able to extract all the liquid using just a chinois (fine mesh strainer) since you can't press the solids hard enough in the chinois. The first pressing is called coconut cream since is the most rich. You can repeat the process one more time, to get a slightly thinner less rich milk (coconut milk).
Coconut milk from the second pressing can be used to soak Thai sticky rice (e.g. for Thai Coconut Milk Sticky Rice with Mango).
Coconut milk spoils easily (in just a few days), so use it soon after it is made. If the coconut milk or the coconut solids have a sour taste then it is spoiled; the coconut meat, cream, and milk should have a sweet taste if it is still good. Store in the refrigerator.
Frozen coconut meat. It is easiest if you defrost this package in the refrigerator the night before you want to make coconut milk. This is about 2 cups of grated coconut.
Coconut cream (first pressing). 2 cups of hot water was added to 2 cups of grated coconut; this made a little more then 3 cups of coconut cream (the grated coconut package says that it has some water in it). This sat in the refrigerator overnight, so the thickest part of the cream has separated and is floating on the top.
Coconut milk (from the second pressing). 2 cups of hot water was added to the squeezed out coconut solids; this made about 2 cups of coconut milk. This coconut milk has sat in the fridge overnight, so the richer part of the milk is floating on top. You can see that it is much less rich then the first pressing.
The coconut milk from second pressing has only a thin film of separation:
If you don't want to make your own coconut milk, you can used canned coconut milk as long as it isn't homogenized (see Kasma Loha-unchit's recommendations on canned coconut milk and SheSimmer's recommendations for canned coconut milk), or you can use frozen coconut milk, which is my favorite.