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The first step is covering notation. The easiest way to think about this in relation to how you hold the cube. Each of the 6 sides are assigned a name related to their position when held out in front of you. Imagine putting a hand on either side of the cube. Your left hand is on the Left side of the cube, your right hand on the Right side. The side between your fingertips is the Back of the cube, the side between your wrists is the Front. Looking down on the cube you see the Up side and opposite of that is the Down side. Each of these sides is assigned a single letter for use in algorithms. The letter assigned is simply the first letter of their name as shown below.
  • L - Left side
  • R - Right side
  • F - Front side
  • B - Back side
  • U - Up side
  • D - Down side
The notations above are pretty standard and you'll find them in most of the other guides out there. For my guide I want to include 2 additional notations which are not widely used, H and V. H is for the middle horizontal layer (slice) located between the Up and Down sides. V is middle vertical slice located between the Left and Right sides. I find it much easier to use these in my algorithms rather than trying to tell someone to move opposing sides and rotate the cube in their hand. I'll explain that further in the next section.
Each move is simply a 90 degree rotation (1/4 turn) of a side or slice. To make things consistent each move will be considered either clockwise or counter-clockwise relative to the current position of the cube. You need to picture looking directly at the face of a side when determining which direction to make the rotation. Clockwise movements are notated by use of the letters given in the list above. A counter-clockwise movement is indicated by use of a Prime (single quotation) symbol after the letter. For example, if we were to take our cube as shown above and perform the move F, this would be a 1/4 clockwise rotation of the Front face. The move B indicates a 1/4 clockwise rotation (as if we were viewing the face) of the Back side. An illustrated example for these moves and several others are shown below.
As I stated above, I want to include 2 additional notations, H and V. H will move in the same direction as U, and V will move in the same direction as L. Those are shown below. I used H for horizontal and V for vertical. I have now seen that the proper notation is E for the horizontal and M for the vertical slices. I'm leaving my notation as is, but keep this in mind if you see these references on another site.
One last note. In the case where you need to rotate a side twice it really makes no difference which direction you move. A double rotation clockwise is the same as a double rotation counter-clockwise. For my notations I will show a double rotation by showing the move 'squared' using the ² symbol. For example, a double rotation of the Front face will be F².

When I first wrote this guide, I spent a lot of time in Photoshop doing these illustrations. I've since come across a nice java applet for the 3x3x3 cube which I think will make it easier for you to understand exactly what is happening. You can use this applet by going to the Notation page.

Once you've covered the notation and the moves you can proceed on to Solving the First Layer starting with the Top Edges.