This means that, given any starting position on the 3x3 Rubik's Cube, there is a sequence of moves, of length at most 20, that solves the starting position. Here, a "move" is to turn a single face 90 or 180 degrees.
Also, and two positions on the Rubik's Cube are at most 20 moves apart.
The superflip, which is a position where all 12 edges have been flipped, is a position where the optimal (shortest) solution has 20 moves. For the vast majority of positions, their optimal solution have less than 20 moves. An algorithm for solving the superflip is U R2 F B R B2 R U2 L B2 R U' D' R2 F R' L B2 U2 F2.
Typically, the red and orange faces are opposite, the white and yellow faces are opposite, and the green and blue faces are opposite. Pairs of colors which tend to look similar are placed on opposite faces.
Furthermore, if you hold the white face on top and the green face towards you, then the red face will be on your right.
The fastest algorithm is not necessarily the shortest.
An example is the U-perm, which can be solved in 9 moves by F2 U' R' L F2 R L' U' F2 (that's 7 moves if you use the slice-turn-metric). However, an often preferred algorithm is the longer (in terms of move count, at 11 moves) but more comfortable (and thus faster) R U' R U R U R U R U R2.
If you disassemble a cube and put the pieces back randomly, the probability that the resulting permutation can be solved by turning the sides of the Rubik's Cube is 1/12. This is because it is impossible to do the following by only turning the sides of the Rubik's cube:
A 3x3 cube has approximately 43 quintillion possible states.
To put this into perspective, if one had one standard-sized Rubik's Cube for each permutation, one could cover the Earth's surface 275 times, or stack them in a tower 261 light-years high. (Wikipedia)