How do I extract coconut milk from coconut meat?

1. Empty the water from inside the coconut, as this is not the milk you want.
2. Crack open your coconut and scrape out the meat.
3. In a blender, take about half your meat and roughly 1 1/2 cups of hot water (more or less depending on your desired thickness), and process.
4. Repeat step 3 with the other half of the meat.
5. Place a few layers of cheesecloth over a bowl and strain the milk through.
6. Wrap up the cheesecloth and squeeze the rest of the milk out.

No special press or tools needed. However, some sort of press could help get the last few drops out when squeezing the mass through the cheesecloth.

I don't think the water necessarily has to be hot. Some sources say to just use water, while other say hot. You may also want to start out with just 1/2 cup water and see how much it yields. Keep in mind: coconuts aren't super juicy. So expect the yield to be roughly equivalent to the amount of water used.

The flesh is still perfectly usable, but its applications may be limited based on how much you processed it (in terms of size).

This site has the step-by-step I used with a few (albeit not very helpful) pictures.

1. Break Coconut

2. Remove the meat from coconut carefully using knife or use desiccated coconut then grind the meat in blender with some water or other option is to scrape coconut meat carefully.

3. If you are using scraped/grated coconut, add some water into it and keep aside for 5 minutes. (coconut extract will dissolve into water)

4. Filter coconut+water mixture in a cheese cloth/muslin cloth (even plain cotton cloth works too).

5. Nutritious Coconut Milk is ready. You can use the milk in cooking or drink it by itself. Pinch of Cardamom powder or pepper powder tastes amazing with coconut milk.

Source: Homemade Coconut Milk Preparation

In this method, nutritions will not get lost, so you can get the fresh and healthy milk.

The best home way. Put meat in a heavy cotton bag. White bag is best. With a ring in the center of the bottom. A draw string top. Close bag & hang up. Move all meat to bottom of bag. Insert stick in bags bottom ring & turn then twist tight. Let milk drain threw bag into pan. About the same as pressing whey water out of curds to make cheese. Meat needs to be in strings when cutting out of hull. This is for fresh coconuts normally done right in the grove. Bag hung to a mango tree. As we raise both together. Our bag is a long pyramid in shape 4 sides. But other bags will work. Mabe a white cotton pillow case for smallamount.