This is my newest instructable and I have recently gotten into rubiks cubes, so, here is how I learned to solve the 2 by 2 rubik's cube. I hope you can understand all of the things that I am saying in this instructable.
Step 1: Shuffle
The first step to solving your rubiks cube is to shuffle the cube. This means that you mix it up so that you can solve it. Before we continue, you need to know how to read an algorithm.
Here is how:
L is for moving the left face clockwise,
L' is for moving the left face counterclockwise.
U is for moving the top face clockwise,
U' is for moving the top face counterclockwise.
R is for moving the right face clockwise,
R' is for moving the right face counterclockwise.
The last one is D for the bottom face clockwise,
D' for the bottom face counterclockwise.
This is an annotation for the rubiks cube.
A good shuffle that I have found is: L' U' L' U' F'. But, you don't have to shuffle it this way to solve the cube, just mix it up pretty good.
Step 2: Solve the First Side Part 1
Now, we have to solve the first side. We do this by first getting a pair of the same color. I like to use white because it is the most stand outish color. You can usually get the pair just by turning once. Afterwards, your cube should look like the picture.
Step 3: Solve the First Side Part 2
Then we have to get the third piece in the top face. The way we do this is to twist the bottom half and put it in the right spot like the first picture, and then move it up into the right spot like the second picture.
Step 4: Solve the First Side Part 3
To finish the first side, put the last piece into the right position like the videos.
Step 5: The Ring Algorithm
For this, you will need to know the first algorithm. To start, all you need to do is face the side with the already solved pair away from you like the first picture. Then do the following algorithm, R' D' R L D L' R' D' R. This is using the annotation i showed earlier. BUUUUT....... if your cube doesn't have a pair, like the first picture, take any side and do the algorithm. Then, you will have a pair and continue with the earlier part. Facing the pair away from you and do the algorithm above. Now you will have a ring like the video.
Step 6: Aligning the Top Half Part 1
Now you need to flip the cube so that the solved side is facing down like the picture. Then, all you have to do is twist the top half until one of the corners matches the ring. The corner closest to you is the matched corner because it needs the color yellow on top because it is the opposite of white, blue and red because the ring at the bottom has those colors.
Step 7: Aligning the Top Half Part 2
Now you need to do the next algorithm. Find a corner that is wrong. Face it towards you so that it is in the left half of the front face. Then do this algorithm, L' U' L F U F' L' U L U U. This will flip the corners. Do this until the corners are all in the right spots. It should look like the picture.
Step 8: Orientating the Corners Part 1
Now, this is the last part, and you need to orientate the corners, or flip them through algorithms. This will solve the Rubiks Cube. First, find a solved corner, (it looks like the first picture, and the corner closest to you is the solved corner). Then, put it in the lower left hand corner of the top face this should look like the second picture. DO NOT TWIST ANYTHING TO PUT THE SOLVED CORNER IN THE RIGHT SPOT. JUST MOVE THE CUBE IN YOUR HANDS.
Step 9: Orientating the Corners Part 2
Now you need to do the following algorithm, R U R' U R U U R U U. Then, keep finding the solved corner, and putting it in the lower left hand corner of the top face and repeating this algorithm, and you should end up solving it. BUT............ if your cube looks like the first picture, just choose either of the two corners and put them in the lower left hand corner of the top face and continue like normal. BUT A SECOND TIME........... if your cube looks like the second picture, where it has two already solved corners, putting them in the lower left hand corner of the top face and doing the algorithm will not work. Instead, you need to face them away from you and then continue with the algorithm. BUT FOR A THIRD TIME............. If you cube looks like the third picture, and it doesn't have any solved corners, then you will need to just pick a side and continue solving.
Step 10: Done
YAY! you have now solved your 2 by2 rubiks cube. I hope you all enjoyed this instructable, and were able to solve your cube.