Basic Concepts in Cubing
The cube is not just a collection of 54 stickers. It's 20 pieces (8 corners, 12 edges) + a core. Each individual piece, called a cubie, is unique. The centers cannot move from their positions. Therefore, using the centers, one can easily deduce the unique locations for each cubie in a solved state. The green-red edge goes between the green and the red center, for example.
The most common method of solving the Rubik's cube is called CFOP (or Fridrich). CFOP (pronounced either as see-fopp, by just saying the letters) is an acronym standing for the four steps involved: Cross, First two layers (F2L), Orientation of Last Layer (OLL), Permutation of Last Layer (PLL). Typically, the cross and F2L are done intuitively, while OLL and PLL are done by pattern recognition and muscle memory, via algorithms*. OLL has 57 different cases and PLL has 21. People starting to learn usually break these steps down into further subsets instead of learning the whole method at once. A typical way to break this down is into 4 separate steps. Each step uses one algorithm multiple times to reach the desired state. One algorithm is used for OLL edges, another algorithm for OLL corners, one or two algorithms for PLL corners, and one last algorithm for PLL edges. This can therefore reduce the number of last layer algorithms to remember from 78 to a mere 4. As a cuber progresses, he or she can learn additional algorithms for each case (for the sake of efficiency), eventually (if he or she chooses to) building up to the full method.
*algorithms in cubing generally refer to a pre-memorized sequence of moves that affect a cube in a certain way. For example, one algorithm might swap the positions of 3 corners while leaving everything else unchanged.
Considered the best for beginners.
Simplified as far as possible - this is for people who just want to be able to solve it, but do not at all care about speed. It is marginally easier than the first link, but is less efficient and promotes less understanding.