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 formulas, 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 of 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 colors of the other stickers on the edges are in this order: blue, red, green, orange. Don't forget to align the center's pieces of the cube!
First two layers (F2L) Edit
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.
1 Here, be sure to insert the pair that is already formed using U'F'UF (or FR'F'R), but not RUR', which would destroy the pair.
2 For this one, R will join the pair, then UR' will insert it.
3 You can "hide" the corner using F', then U2F will join the pair, then this becomes case 1 to the left. This differs from case 2 only by the orientation of the edge (blue is up, not orange)
4 This can be solved with URU'R' (join the pair) then U'F'UF (insert the pair)
5 Here, the white side of the corner is facing up. To join the pair, UR will move the edge into a position where the corner can attach to it properly, then U will join the pair and R' will put it on the top. Now insert the pair into its slot.
6 In cases where the pair is joined wrong, the strategy is to separate the pair and turn it into another case. If you do UF'U2, you can turn this case into case 2 above. If you do RU2R', you can turn this into case 3.
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.