The colors shown in the diagrams are identical to those of the original Gear Cube.
Gray indicates that the color present in that location is not relevant to the puzzle. Similarly, a hidden piece indicates that the piece present in that location is not relevant to the puzzle. This makes it much easier to understand.
Examples:
If I tell you that only the second and third layers remain to be solved, it is easier to understand with this diagram:
Rather than with this one:
The movements:
They are noted in English because that is the international convention.
This is a 90° movement when looking at the layer in question.
The following examples show the rotation clockwise and then counterclockwise.