The easiest way to move checkers is to "drag and drop." Put your mouse pointer over a checker you want to move, press the left mouse button and drag the checker to the desired point, holding down the button while dragging.
If you prefer to use mouse clicks, the left mouse button is for the left die shown on your board. Right click your mouse for the right die.
If you always want the higher number displayed on the left, go to the menu Settings->Appearance-> General and select Show higher die on left.