Step 1: Solving the White Side, Plus a Continuous Line Around the Top
Start the white side on any side that has. a white piece. From there, you want to look at all the white pieces on the cube. Match up the white pieces on the top by using the algorithm: Ri, Di, R, D. You have to get all the white pieces on the top face, as well as having a continuous line of green, red, blue, and purple (or black depending on your cube) right underneath the white layer. Accomplishing this can be done with common sense, and figuring out where the corners have to go in order to match up correctly.
Step 2: Solving the Yellow Layer
Now with the white side and colored layer completed, turn your cube over. If you have one yellow piece, position that in the bottom left corner and do the following algorithm: R, U, Ri, U, R, U2, Ri. (U2 is up 2 times. After the algorithm put the yellow piece(s) in the bottom left again and do the algorithm again and keep doing this until the yellow side is complete.
Step 3: Orienting the Last Corners
Turn the cube until a pair of colors (like red or blue, that are together) matches up with a pair of the same colors from under the white layer,creating a complete side. By now, you should have 3 sides solved. LAST STEP: Turn that solved side (whatever color it is) to the back side and do this algorithm: Ri, F, Ri, B2, R, Fi, Ri, B2, R2
Step 4: You're Done!!
Congratulations! You've completed the 2x2. You make now wave your hands in the air like you just don't care. :) Your welcome.