Everything I've read indicates that a compost pile should be moist, but that any excess water should be able to drain away. Don't put your compost material in the lowest spot of the yard.
If rain is not providing your compost pile with enough moisture, you will need to add some water yourself. Collecting rainwater is a good practice, because rain is generally close to pH neutral and has no added flouride or other chemicals.
I do not add additional moisture to my heap unless there is an extended drought. Simple reason is that I don't have time to worry about it. I'll use it when it breaks down, but I'm not really helping the process along as much as many folks will.
A good working temperature for your active compost pile...
“The bacteria and other critters that are responsible for the breakdown in a compost pile are aerobic creatures. Air flow in the pile is essential or the aerobic critters will die.”
That right there is the reason to turn the compost pile.
I have read that some people use PVC pipe drilled with many holes placed into the middle of the pile with the open ends sticking out of the sides in an attempt to get O2 into the pile.