Before the beginning I want to say that I am german, so when I have any spelling-mistaces please tell me. I also wnated to say that I developed this movments on my on.
Step 1: Before beginning
Before beginning you should know what the movments mean. If there are only the letters turn it clockwise, if there is the letter and ' turn counterclockwise.
Step 3: 1st Layer
Step 4: Swap cornerpieces
The algyrithmus is:
B U B' U' B' L B L'
Now the cornerpieces should have the right possison.
Step 5: Turn cornerpieces
Here is the Algurythmus:
L U' L' U L U' L' D L U L' U' L U L' D'
now you done it! You solved the 2 by 2 by 2 rubiks cube!