Coconut milk is such a vital ingredient in a lot of filipino recipes specially those that are of Bicolano origin. I've read some blogs and recipes that recommend adding water prior to extracting the coconut milk/cream. Personally, I don't recommend it. That's because it will just dilute the cream and will not taste as "creamy" as it should. Anyway, it's quite easy to add water if you really must. Just be sure you add a maximum of 2 cups per coconut.
There's an advantage to adding water though. Some say it's easier to extract the milk. Well, that's not quite accurate. It makes it easier to squeeze the grated coconut but not to extract the milk/cream from it. The technique in manual extraction is to squeeze the coconut hard several times so that its juices come out. A final squeeze (after about 5 times of squeezing it right in the container) is to get the juice out and to make the juice pass through a sieve so that any meat that is left will be filtered.
Another thing about cooking with coconut cream is to treat it like real milk - you can't leave it to boil without mixing it or the oil will separate from its water component. That's if you are not trying to make latik or extract the oil for cooking. But if you do intend to extract the latik you shouldn't mix the coconut milk too much. Not touching it at all before the oil starts to surface is even better.
I've found a good blog about this. You may want to browse through Pinoy Food Recipes.