How to Solve the Rubik's Cube/CFOP
The Fridrich method or the CFOP method (cross, F2L, OLL, PLL) is a fast method for solving the Rubik's Cube created by Jessica Fridrich. It consists of four steps: Cross, F2L (First Two Layers), OLL (Orient Last Layer), and PLL (Permute Last Layer). Although it requires you to memorise many (up to 78) different algorithms, it's one of the fastest speedcubing methods.
It is recommended that you should start learning using the beginner method first, then use the Fridrich method once you have become proficient at that.
The cross is done intuitively. It is usually done starting with the white colored squares. You should do it on the bottom because then it's easier to locate the other pieces. The cross is done in eight moves or less (this will take a couple days of practicing), though in over 99%of the cases it can be done in 6 moves. A tip for training is to do the cross blindfolded. This will allow you to focus on the next step, F2L while doing the cross. Make sure that the colours of the other stickers on the edges are in this order: blue, red, green, orange. Don't forget to align the centers pieces of the cube!
First two layers (F2L)
The strategy here is to join a corner of the first layer with the edge that goes above it, then insert that pair. The cases for this step can all be solved intuitively if you have enough experience. The cases described below are designed to help you gain that intuition.
There are, of course, many more cases than this, but most can be solved with the strategies above or can be reduced to one of the above cases.