Cross 
F2L 
Orientation 
Permutation 

This is the Fridrich method created by Jessica Fridrich. With this method you can solve the cube on average using about 56 moves and under 20 secods. First you make a cross on the bottom face, this usually takes about 6 moves. Then you solve the F2L(first 2 layers). Each corner and edge pair takes about 7 moves, so it usually takes about 28 moves for that. Now you only have 1 layer left. This last layer will be solved using 2 algorithms (an algorithm is a set of moves that accomplishes a certain goal on the cube). First you orient the entire last layer using 1 algorithm (meaning you flip over all the last layer cubes making the last layer 1 solid color). Then you permute the last layer with 1 algorithm and the cube is solved. There is a total of 57 orintation algorithms and there is 21 permutation algorithms. Don't let this number intimidate you, once you get the hang of memorizing these algorithms it gets very easy. When learning these algorithms don't rush them, learn a few, then make sure you master them, then learn a few more.
Cross 
F2L 
Orientation Algorithms 
Permutation Algorithms 