OK, so for those of you who get confused on what hand coordinate system you are using or switching to and what rotation you are going to be on. Here are some images that i found to help illustrate this better for you.

Left Handed System

Right Handed System

Rotation

When you are trying to figure out which way you are rotating, all you have to do is to determine which hand coordinate system you are in, then looking at that hand, look to see what direction your fingers are pointing toward. its that simple. So for example, if you are in a left handed coordinate system, look at your left hand with your thumb pointing up. Your fingers are warping around and pointing in. if you were to stick your fingers out and them bring them back in again, you would see that they are moving back and forth in a clock wise motion. This indicates that you would be rotating in a clockwise direction. 

To better get you acquainted with this concept, here are some problems that you can solve to help you understand. Move your hands using the images above to figure out what hand coordinate system it would be. 

1. North +Y, East +X, Up +Z

2. South +Y, East +X, UP +Z

3. North +Y, East +X, Down +Z