Rubik's Cube Solution Guide
First Layer Edges (The Cross)
  1. — Position white center to top face
  2. — Pick any top face edge cube and bring it to the top
  3. — If properly oriented with front face center, move on. Otherwise...
    1. — F U' R U
  4. — Repeat steps 2 & 3 above until all four top face edges are in place
First Layer Corners
  1. — Two simple moves when white square is on the bottom row Front or Right face:
    1. — Front: F D F'
    2. — Right: R' D' R
  2. — Otherwise white square is on the bottom: R' D2 R D — then do step "b" above
Second Layer Edges
TURN THE CUBE OVER, SO THAT THE ALREADY-SOLVED WHITE FACE IS ON THE BOTTOM.

Solving the middle layer edges requires memorizing a simple string of moves with one possible variation.
  1. — If present, find an edge cube in the top layer that needs to be moved to the middle layer and move it to the front.
    1. — If top color == left, move it to right edge of top face, then: F U2 R U R' U2 F'
    2. — If top color == front: F U2 R U' R' U2 F'
    3. — ( Note the single variation in the two strings above )
    4. — Repeat step "1" while applicable
  2. — Otherwise, move a middle edge (on the left) up to the top using the string in step "b" above, then repeat step "1"
Chris Bandy's Third Layer Solution

Third Layer Edges
First, look at the position of the blue squares on the top layer. There are four possible arrangements:
  1. — Dot
  2. — El
  3. — Bar
  4. — Cross
The blue Cross is the goal. Do the following "Face" algorithm repeatedly until the cross is present. If the "El" is visibile, rotate the top layer so that the "El" is backwards and in the top left of the upper face. THIS DOES NOT MEAN TO ROTATE THE ORIENTATION OF THE CUBE, IT MEANS TO ROTATE THE TOP LAYER ONLY.

The "Face" algorithm...
  1. — F R U R' U' F'
Once the cross is achieved, rotate the top layer until two edges are correctly placed.

If the correct edges are in opposing positions, hold the cube in any orientation (with the blue face up). If the correct edges are adjacent, hold the cube so that those two edges are to the back and to the right sides. Then perform the following "Push" algorithm.

The "Push" algorithm...
  1. — R U R' U R U2 R' U
That should put the edges right.

The last step is to fix the corners...
Chris Bandy's Third Layer Solution starts at 03:12

Third Layer Corners
First, find one corner that is in the right place. Hold the cube so that the correctly placed cube is in the top right corner of the front face and perform the "Dodge" algorithm.

The "Dodge" algorithm...
  1. — U R U' L' U R' U' L
If none of the corners are in the right place, do the "Dodge" algorithm on any corner. This will move one of the corners into the right place, then repeat the "Dodge" algorithm again with the correct corner in the upper right of the front face.

When all of the corners are in their correct place, unless you get lucky some of the corners will be twisted wrong. Again, face one of these corners so that it is in the top right AND LOOK AT THE OTHER CORNER WHICH WILL BE MOVED NEXT AND MEMORIZE ITS COLORS. Then, perform these 4 moves until the blue face of the current corner is facing up. May have to do it several times...

The "Last Four" moves...
  1. — R' D' R D
When the top right corner has blue facing up, spin the top layer so that the other twisted cube is in the top right and perform the Last Four moves again (and again, if necessary).