SimplyCube

CFOP tutorial
This is a faster but more advanced method of solving the cube. I only recommend learning this once you have mastered the beginner method.
Cross
Just like in the beginner method, this step solves 4 edges to make a cross. So instead, we will learn how to improve how fast you can solve your cross. First you want to solve your cross on the bottom of your cube instead of the top, this is to save the time wasted in cube rotations.
When solving an edge, you want to try to make those moves setup another edge for insertion. This is commonly done by placing an edge over an edge you are about to insert.

U

F

R'

Also try to visualize how you are going to solve your cross before starting to lessen the pauses in your solve.
F2L
Unlike in beginner method which solves the first layer of the cube, F2l solves 2 layers at a time. First find an edge that belongs to the middle layer and an edge that goes on the bottom layer. both these peices have to have the same colors. If these pieces are not on the top layer, use (R U R' U) or (L' U' L U) to move them to the top.

(R U R' U')

(L' U' L U)

Split

Join

Then find a way to move the pieces so its either a split or a join pair.

U

R

U2

R'

Finaly this step soves the pair and inserts it on the middle and bottom layer. Depending on whether you got a split or a join pair there is an algorithm to solve them. Do all of the steps above again until the 2 bottom layers are solved.
Split

R

U

R'

Join

U

R

U'

R'

OLL
This step solves the whole top face so its one solid color. There are a total of 57 cases and algorithms to memorize and can be found here: .
PLL
This step swaps the top layer pieces to solve the cube. Just like the OLL step, there are a total of 21 cases and algorithms to memorize and can be found here: .
Source to images