How To Solve The Second Layer Of The Rubik's Cube (F2L)
Now that we've finished the white face, let's turn the cube upside down because we don't need to see the solved side anymore.
The solution of the Rubik's Cube could be done intuitively until this point but this is where most people get stuck. The reason for that is that you would have to foresee too many steps to complete the first two layers (F2L).
We have to learn two algorithms which are symmetric to each other. We call them Left and Right algorithms.
The Left algorithm sends the edge piece from the Front-Up position to the left side while the Right algorithm sends it to the right as marked with the arrows.
U' L' U L U F U' F'
U R U' R' U' F' U F
When there's no edge piece to insert into the middle layer you will have to execute the algorithm twice to pop the piece out in the first step.
For example, when the edge is on its place but turned incorrectly:
U R U' R' U' F' U F - U2 - U R U' R' U' F' U F
At the end of this step your cube should have the middle layer solved and an intact white face at the bottom.