Before you start solving a Rubik's Cube, there are a few things you should know beforehand in order to comprehend the algorithms and instructions.
First, the color of any given side of the Rubik's cube is determined by the center piece. In the photo, you can see that the center piece is blue, so that particular side is the blue side of the cube. The center pieces never change their orientation, so it is important to know what color a particular side needs to be.
Second, you will need to understand the abbreviations for the algorithms. F, L, R, U, D, and B refer to the front, left, right, up, down, and back faces respectively. An individual letter means one rotation clockwise (for example, F means rotate the front face once clockwise) whereas a letter followed by an apostrophe means one rotation counterclockwise (for example, F' means rotate the front face once counterclockwise).
Now you are ready to begin!
Step 1: Solving the Cross
The Rubik's cube can be solved starting at any side. Once you have chosen a side, the first step to start solving is completing a cross as shown in the picture. Note that the colors match on all faces, not only on the cross but the side pieces as well (the blue/red and blue/white pieces align with the red and white faces).
This step can be done without algorithms, and is better to learn without algorithms as there are many ways the cube can be arranged prior to beginning this step.
Step 2: Solving the First Face
Once you have completed the cross, you may now fill out the corners of your first face. You first need to determine what piece needs to go in each corner. Each corner will have the colors of the 3 faces that surround the corner. Align the respective piece on the bottom row beneath where it needs to be and orient the cube such that the solving side's color on the piece is facing you (the side facing you is now considered F). Perform one of two following algorithms depending on whether the piece is on the left or right.
If it is on the right: D'R'DR
If it is on the left: D'LDL'
Repeat these algorithms until you have solved your first side. The first two pictures show the before and after of performing the algorithm on the left side. In these photos, the yellow face would be considered F. The third picture shows the end result.
Step 3: Solving the Center Layer
Now you will need to turn your Rubik's cube over such that the face you just solved is on the bottom. We will now be focused on solving the center layer. There can be up to 4 edge pieces (pieces with only two sides) missing. You will first need to align any missing piece such that one of the faces is matching on the correct side. In the first photo, you can see that the red/white piece is missing, so we align the red/white piece such that white sides match up.
Orient the cube such that the space where the edge piece needs to go is on your right. In this case, that would mean the red face is considered F, which would put the spot where the red/white piece needs to go on the right. Depending on where the aligned edge piece is, you will need to perform one of two algorithms.
If the missing edge piece is aligned on F: URUR'U'F'U'F
If the missing edge piece is aligned on R: U'F'U'FURUR'
The second photo shows the result of performing this algorithm on the cube in the first photo. You will see that the red/white piece is now where it needs to be. Repeat until the center layer is solved.
In some cases, the edge piece will already be in the spot it needs to be, but it will be oriented the wrong way. Simply perform either of these two algorithms to "pop" the piece out, re-orient it, and then perform the necessary algorithm.
Step 4: Solving the Top Face 1
Next, we will solve the top face. The first think you need to look for is either a small L shape or line on the top face and perform one of the following algorithms, treating the top side as U (in this case, green).
Orient the L on the top left corner of the face: FURU'R'F'
Orient the line so that it is horizontal to you: FRUR'U'F'
If neither of these shapes can be found, perform either of the algorithms at random and one of the shapes should appear.
In the pictures, you can see that the green side containing both the bar and L shapes. Note that the shapes can sometimes be slightly clouded, with other colored pieces, as with the L shape.
Step 5: Solving the Top Face 2
Once the previous algorithm has been performed, we will orient the cube such that a green color is always on the top left side of the front face (with green still being considered U). In the photo, the white side would be considered F. Perform the following algorithm until you can no longer create the aforementioned scenario:
You will know that you are done performing this algorithm when green pieces can only be found on the top right of each face, and the top side resembles a fish shape. Orient the cube such that the fish is facing the bottom left and perform the following algorithm (in the photo, yellow would be considered F)
Voila! The top side should be solved.
Step 6: Solving the Final Layer 1
The first part of solving the final layer will be putting all the corner pieces in place. Rotate the top side until only one corner piece is in the correct spot. In the photo, only the green/orange/yellow corner is in place. Put this corner on the left side and perform the following algorithm:
Repeat this algorithm until all corner pieces are in place. Sometimes, either 2 corner pieces or no corner pieces will be in place. Orient the top side so that no corner pieces are in place and perform this algorithm once. Then, re-orient the top side such that one corner piece is in place and start from the beginning of this step.
Step 7: Solving the Final Layer 2
Now all we have to do is put the final edge pieces in place. Orient the cube such that one solved side is on the right (in this case, red is R). Perform the following algorithm until the cube is solved:
And that's it! You have solved your first Rubik's cube!.