There is a notation used in describing the movements you are doing on the cube:

Front face: F
Back face: B
Top face: U
Bottom face: D
Right face: R
Left face: L

In a sequence, each of these letters tells you to move the corresponding face 90 degrees clockwise. A letter with an apostrophe, e.g. U', tells you to move that face anti-clockwise. This would be said 'anti-up'. A letter with a 2, e.g. U2, tells you to move that face twice in either direction, as direction doesn't usually matter.
It is important to remember that the moves are done if you were looking directly at the face.

These letters are used in sequences known as algorithms, which are sets of instructions that achieve a specific goal. For example, from a solved state the algorithm F2 B2 U2 D2 L2 R2 would achieve a pretty pattern like such:

Other, less common letters for notation include M, E, S, x, y, z and lower case for all of the normal faces.
M: Face between L and R
E: Face between U and D
S: Face between F and B
x: Rotate the cube up (as if you are doing R, but move the whole cube)
y: Rotate the cube to the left (like doing U, but move the whole cube)
z: Rotate the cube on its side to the right (like doing F, but move the whole cube)

A lower case letter of any normal face means turn two faces, i.e. the one you are turning and the middle face next to it at the same time:
f: F and S
b: B and S
u: U and E
d: D and E
r: R and M
l: L and M

We will only be using the standard 6 for the beginner's guide.
Also, each individual piece is called a 'cubie'.