To move using the mouse, click the left or right mouse button on any colored sticker on any cubie in the view, hold the button down, drag and let go.

When using the left mouse button, the sticker and a whole slice of the cube will move in the direction you indicated. The slice tilts slightly to help you see what will happen when you let go. If you are not happy with that, just move the mouse back to where you started.

If you are using the right mouse button, the mouse pointer sticks to the cube and the whole cube rotates with it until you release the button.