Using Fresh Cocoanut Milk?
Scrape the flesh out of a green (with husk) or brown coconut and toss into a blender. Add about half a cup of warm water; blend; and then squeeze out and strain the liquid (coconut cream) through a cheesecloth. A second run with about a cup more of warm water gives you (thinner) coconut milk. In most places (and if you don't have a blender or want to do it the traditional way), coconut is grated out of the nut when removing the flesh. The grated meat is then squeezed and kneaded in the water and then strained to get the cream and milk.
"Yielding milk" sounds a little ambiguous. You do know that you'll have to create the coconut milk, right? When you crack one open, the stuff inside is coconut water. Coconut milk is made by pressing the meat.
I've never made my own, and have no idea how much you should get per fruit, just thought it sounded a little ambiguous.
Gordeaux is right.
To make coconut milk you have
1) drain out and reserve the coconut water and then
2) chip out the coconut meat from the shell, finely shred or grate it, let it soak in warm water for a while. Then press out the "first milk" (this will be thicker and richer). Then put the solid matter back in some more warm water, soak and press again to yield "second milk" (thinner, also has its uses). Or mix the first and second milk.
You don't have to buy green coconuts for this. You can buy the regular brown coconuts (which are simply the green coconuts from which the brown husk has been peeled off).
Coconuts sold green are indeed younger and more tender, and have more water and the meat is not fully formed and is oyster-like in consistency. You can't extract coconut milk from this (or at least I've never seen a method to do so).
The brown coconuts are what you need.
I've also never made this from scratch. Is there something in kashruth against using canned coconut milk?