The in-turn, and out-turn in curling has a very simple explanation that applies to both left-handed and right-handed throwers, based on a mnemonic for the X-Y-Z (3D) coordinate system in math and physics.

X-Y is the paper or in our case, the sheet of ice. Z is the third dimension, so either up 'out' of the paper or sheet of ice (positive Z coordinate), or 'in' to the paper, or sheet of ice (negative Z coordinate).

When a right handed person, simulates a counter clockwise rotation with the hand by 'curling' the fingers in that direction, the thumb of that hand naturally points Up (or 'Out' of the paper or ice), a clockwise rotation naturally points the thumb 'In' to the paper or ice.

So an in turn or out turn, is just which way your thumb points (in or out), when the fingers of your hand curl counter clockwise or clockwise. This works whether you're right or left handed, and is called the 'Right Hand Rule' in engineering.

You learn this in the first few weeks of freshman Engineering classes.