Layer By Layer
The Layer By Layer method involves solving the 2x2 cube layer by layer. The first layer is simple to do so as a 2x2 does not have a center piece like a 3x3. Below is a brief summary of the steps with a video linked at the end,
The first layer involves solving the 4 corners,
which will result in one side of the cube being solved,
in this case green. The next step would be to permutate the corners.
Moving the top layer will result in one or two corners permutated into their respective corners.
Next, only one algorithm is needed to permutate the remaining corners.