This is my tutorial on solving the 3x3x3 Rubik's cube. It is a solution sketch that is simple to execute and easy to remember. It is by no means the most optimal method to solve the Rubik's cube. Below there are pictures of the final position of the cube, the notation of the cube faces used throughout this guide and the color scheme that the cube is assumed to have.

Hold the cube so that the white center is at the top (U). Intuitively solve the white cross by placing the edges of the top layer in their correct position and with the correct orientation. After this step the cube should look like the image below:

Now turn the cube around so that the completed white cross is at the bottom layer.

Intuitively place the white layer corners in order to complete the first layer. There are 3 cases after you place a corner piece above the correct position. If the corner is already placed in the correct position but in the wrong orientation use some other algorithm, for example R U R' U' to get it out of the bottom layer.

Repeat for all 4 edges (3 more) until you have solved the bottom layer completely:

Now we will place the second layer edge pieces. Find an edge piece on the top layer that doesn't contain yellow. If no such piece exists, remove one such piece from the middle layer and place it in the top layer. For this step, one option would be to place this piece on the right side of the front face and execute the following algorithm:

The final U-turn of the algorithm is not important and is only present for more convenient presentation (otherwise the resulting edge piece would be on the back face). You should now have at least one edge piece without a yellow sticker on the middle layer (if you didn't have before). Align this piece with its respective color on the middle layer and figure out whether the face with the center whose color is the same as the sticker of the edge piece in the top layer is on the R face or the L face. If it is in the R face execute the following algorithm:

If it is in the L face execute the following algorithm:

Repeat for the 3 remaining edge pieces to complete the middle layer. At this point you should have completed the bottom two layers as shown in this image:

In this step, we create the yellow cross on the top layer. The edge pieces of the cross need not be aligned
with the respective sides of the cube, so we will only focus on the top face. The top face can either have all 4
edges solved, 2 edges solved or no edges solved. Use the state diagram below, which only shows the top face, to
reach the final solved state of the cross by repeating the algorithm `F R U R' U' F'`

that performs
the transition between the states. If necessary, rotate the cube or perform U-turns to reach isomorphic
positions.

You should now have a completed yellow cross:

During this step, the top layer edge pieces are repositioned so that the yellow cross is aligned. Start by performing U-turns until two edge pieces are correctly aligned; this situation is always possible. If all 4 edges happen to be aligned, you can skip this step. The following image shows a correctly placed edge piece (F face) and an incorrectly placed one (R face).

Rotate the cube so that the two incorrect edges are on the front and right faces. If the incorrect edges are opposite each other, hold the cube in an arbitrary way. Use the following algorithm to swap the top layer edges that are on the front and right faces.

You will have to execute the above algorithm more than once if the incorrect edges were opposite each other. Do this by performing U-turns until two edge pieces are correctly placed first.

You should now have a cube with a completed and aligned yellow cross:

In this step, we will place the 4 top layer corners at their correct positions but not necessarily their correct orientation. In the following images, one corner is correctly placed in the FRU position (left) and one corner is incorrectly placed in the same position (right).

Find a correctly placed corner and rotate the cube so that it is in the FRU position. If no corner is correctly
placed, hold the cube in an arbitrary way. Perform the algorithm `L' U R U' L U R' U'`

, which
maintains the position of the FRU corner and shuffles the other 3 corners. You may have to repeat the algorithm
multiple types in order to get all corners in their correct position but not necessarily their correct
orientation. This may look something similar to the following image:

The final step is to orient the top layer corners in order to finish the puzzle. Hold the cube with one
incorrectly oriented corner piece in the FRU position and execute `R' D' R D`

until it is correctly
oriented. Place another incorrect corner in the FRU position with U-turns and **without turning the cube**.
Repeat the algorithm `R' D' R D`

until the corner is solved. Repeat for all unsolved corners. You
should now have a solved puzzle.