There is a notation used in describing the movements you are doing on the cube:
So each letter tells you to move that face clockwise by 90 degrees, and a letter with an apostrophe tells you to move that face anticlockwise 90 degrees. U', for example, would be said as 'anti-up'. A letter with a 2 tells you to move that face by 180 degrees.
It is important to remember that the moves are done if you were looking directly at the face. Looking down at the cube, it looks like U and D should move the same way, but you have to remember that D is upside-down!
These letters are used in sequences known as algorithms, which are sets of instructions that achieve a specific goal. You just perform each move in the algorithm from left to right. For example, from a solved state the algorithm F2 B2 U2 D2 L2 R2 would achieve a pretty pattern like on the right.
Also, each of the smaller cubes that make up the Rubik's Cube is called a 'cubie'.
That's all you need to know for the beginners guide!
Other, less common letters for notation include x, y, z, M, E, S,and lower case for all of the normal faces:
So x is a whole-cube R, y is a whole-cube U, and z is a whole-cube F. E and S are almost never used, as they can be more easily performed by rotating the cube and doing an M or M'.
A lower case letter means a double layer turn, i.e. the face you are turning and the middle face next to it at the same time: