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The CFOP, mainly known as the Fridrich method is pretty much the best method there is for solving a cube fast. ALL cubers in the top 50 or so use this method. It has 4 steps as the name indicates C-F-O-P. Here is a small intro on the method.
Don't start with the difficult methods (like this one) if you are a beginner, but begin with my BEGINNERS method and a lot of your questions will be answered.
The method exists out of 4 steps of which the last two are simply performing a bunch of sily argorithms.
1. Make a Cross on the bottom (or on top and then turn the cube so that it is the bottom)
PICA Front Side
PICA Back Side
This is what the cube looks like after step 1. It takes a theoretical maximum of 7 moves to get this, but mostly it can be done in 5 or 6 moves. For a beginner it doesn't matter how much moves it cost of course but for speed you must be able to see it quick. It takes a bit practise. To know more about making the cross click the link on top of this page to the first step.
It can be very useful to start with your cross on any colour of the cube, this way the chances of having an easy cross increase!
2. Solve the F2L by solving 4 corner-edge pairs.
PICA front side
PICA back side
This is the main step of the method. Connect a corner and an edge, then solve this "pair". This step takes a lot of practise as well. If this step is good you'll probaly get fast times. Average turns for this step is about 26 turns. It can be done quicker if you know al kinds of shortcuts, but I haven't learn those.
3. OLL, Orientate Last Layer (twist all cubies the right way)
PICA front side
PICA back side
This step has got 57 cases, it seems a lot, but it's not very hard to learn all cases. Most of the cases are mirrors or inverters and can be learned very easily as you will notice at the OLL section. Link on the top.
4. PLL, Permutate Last Layer (put the cubies of the Last Layer in the correct place)
PICA front side
PICA back side
This step has got 21 cases. Some of them are the reverse from an other. It's just learning things from your head and it takes practise to be fast at this step. Also check other websites for other algorithms.