Breif Overview- Beginner's Method
1.) To solve the 3x3 rubiks cube, first you are going to have to solve the cross.
2.) Second, you will solve the corners. After this, the whole first layer, not the side, but the layer will be solved.
3.) Next, you will solve the second layer by filling in the four slots, (the centers are always in the right place).
4.) Next, you will solve a cross on the top side.
5.) Next, you will solve the four crosses on the four middle sides.
6.) Next, you will place the corners in the right places, but not neccesarily oriented correctly.
7.) Lastly, you will orient the corners, thus solving the cube.
1.) Solve the cross
This step is mostly intuitive. What you're going to have to do is solve the cross and have the side-pieces of the cross in the right places so that they form 2x1 bars with the centers, like this:
What you have to do to achieve the cross is to use two different steps. The first is if the piece is right under where it should be, like this:
If it is like this, simply use the algorithm F2. (If you do not know what this means, check the notation tab.) This will get the piece into the right place.
The other case is if the piece is right under where it has to be but is flipped upside down, like this:
Instead, you're going to use this algorithm:
F' U L' U'
Using those two steps, you should be able to end up with a solved cross:
2.) Solve the corners
Now you are going to solve the corners of the first layer. This is your goal:
You are going to put the corner right under where it has to be, like with the cross. Make sure it is under the right slot. There are three possible situations when the piece is right under where it should be. The first is where the red is on the bottom face, like this:
The second possibility is where the red side of the piece is on the right, like this:
The third and last possibilty is that the red side will be on the left, like this:
You are going to have to use one algorithm to solve each of these three positions. Depending on what the situaiton is, you are going to have to use this algorithm one, three, or five times. This is the algorithm:
R' D' R D
If the piece is already in the slot but is not rotated right, you can just use the algorithm 2 or 4 times. If the piece is in the wrong slot, use the algorithm one to get it out and then proceed as normal. This should be enough information for you to solve the first layer of the Rubiks Cube.
END OF PART ONE!!!
Pretty impressive, huh?
The first algorithm is called the right algorithm. (not you got the question right right, but the direction right). You will use this algorithm when your cube looks like this:
It is called the "right" algorithm because in this situation, if the cubie on the U layer goes down and to the right onto the middle layer, it will be in the correct place. The algorithm is:
U R U' R' U' F' U F
The algorithm is:
U' L' U L U F U' F'
Using these two algorithms, you should be able to solve the first two layers of the Rubik's cube
In the next step , you are going to have to solve the cross on the top layer of the Rubik's cube. When you have the first two layers solved, you will have one of four combinations on the top layer, just for the edge pieces. If you include corners, there are 57 possibilities, so don't. They are one dot in the middle,
If you have a cross, you don't have to do anything. However, if you have the single dot, you will have to use this algorithm.
F R U R' U ' F'
After this, rotate the cube until your the top of your cube looks like the L diagram above. Then you will use F R U R' U' F' twice more.
If you have the L, you will use F R U R' U' F' twice to reach the cross.
If you have the line you will use F R U R' U' F' only once.
Next you are going to permute the four edge pieces on top until they are in the right places. When you are done, you will have a solved first and second layer, a cross on top, and the middle pieces of the top layer will all be solved. it will look like this layed out: (Black denotes a color that does not matter)
In any position, if you turn the top layer, you will eventually get a position where two are solved. When you do, position the cube so that the solved pieces are on the R and B faces. When they are like this, use this algorithm:
R U R' U R U U R' U
Sometimes you will get a case where the two solved cross cubies are on opposite faces. Then you will do the algorithm once, and then you can turn the U face twice and use the algorithm again. Now your entire cube should be solved besides the corners on the top face.
In the next step, you will get the corners in the right places, not necessarily the right orientation. To do this, you should find one corner piece that is in the right place. Place that piece in the right-down spot of the top face, and then use the algorithm
U R U' L' U R' U' L