First you need to learn the notation of the Rubix Cube. See picture for demo.
R = Turn the Right face 90 degrees clockwise
D' = Turn the Down face counterclockwise
L2 = Rotate the Left face 180 degrees clockwise
Step 1: Step 1. Solve Yellow Edges
First you need to pick one color and solve the edge pieces. Choose color of your liking but for reference purporses we do the yellow edge pieces first. Your cube should look like picture "Step 1."ste
Use this algorithm to when your cube looks like picture 1.1.
F R' D' R F2
Then use this algorithm when your cube looks like picture 1.2.
F' R' D' R F2
Then use this algorithm when your cube looks like picture 1.3.
R' D' R F2
Step 2: Step 2. Solve Yellow Corners
After this step your cube should look like picture 2.1.
Use this algorithm if your cube looks like picture 2.2.
R' D' R D
You can do the process quicker with this algorithm if your cube looks like pictures 2.3. or 2.4.
F D F' (2.3)
R' D2 R D R' D' R (2.4)
Step 3: Step 3. Solve Middle Layer
If your cube looks like picture 3.1. and you need to move the top blue (or the color you are actually working with) to the right you must use this algorithm:
U R U' R' U' F' U F
If you want to move the top blue from picture 3.1. to the left please use this algorithm:
U' L' U L U F U' F'
If your cube looks like picture 3.2. you must use the following algorithm:
U R U' R' U' F' U F - U2 - U R U' R' U' F' U F
Step 4: Step 4. Top Cross
In this step your cube looks like picture 4.1.
First you need to do the L-shape (see picture) 4.2.
Then Line (see picture 4.3.)
and finally Cross (see picture 4.4.)
All of these are done in sequential order with the same algorithm:
F U R U’ R’ F’
Step 5: 5. Swapping Last Layer Edge Pieces
When you have the top cross there might be a situation that the edge pieces wont match with side colors. See picture 5.1.
To make them match you must use the following algorithm:
R U R' U R U2 R' U
This algorithm only works when you position your cube like in the picture. Once you have completed the algorithm once, you need to turn the cube again to look like in picture 5.1.
Step 6: Step 6. Orienting Last Layer Corners
See picture 6.1.
When your cube looks like in the picture shown in this step you must use the following algorithm to orient corner pieces:
U R U' L' U R' U' L
This algorithm you might need to do atleast twice.
Step 7: Step 7. Your Cube Is Going to Be Solved
See picture 7.1.
All you have to do is use this algorithm until your cube is solved:
R’ D’ R D
Dont worry if your cube looks messed up in between the algorithms and the actual solution.