Blind Guru - Solution 1

The first soltuion for solving the cube.

Step 1 -- Do the first face

The first step involves choosing a color, and getting all the pieces of that color to form a complete face. These must also be in the correct relative location.

First, we will do the edges. Let's say we pick white as the side to complete first (many people choose white as it is the easiest color to pick out). Turn the cube so that the white center piece is on the U face. Note that the centers are attached, so that they are always in the same position with respect to one another, unlike a cube of even degree (i.e. 2 x 2 x 2 or 4 x 4 x 4).

First, we put the edge pieces (those with 2 colors) in the right place. There are several possibilities. Note that when moving pieces around you should have the piece that you are working on the F face.

White/Other color (OC) piece is on the D face. Rotate the D face so that it is directly underneath the place where it needs to go (on the U face). If the white side of the piece is on the D face, apply F², and it will be correct. If the white side of the piece is not on the D face, apply D R F' R'.
White/OC piece is on the center slice (i.e. middle portion of the cube) . Apply F or F' to get the piece on the D face, and then perform above moves.
White/OC piece is in correct position, but incorrectly rotated. Apply F² and do the above moves as necessary.

Second, we do the corners. There are six main possibilities for each of the four corner pieces:

Corner piece in correct place. Do nothing.
Corner piece is in the correct place, but incorrectly rotated, so that the piece needs rotating clockwise. Hold the cube so that this piece is in the URF location, and apply F D F' D' F D F'.
Corner piece is in the correct place, but incorrectly rotated, so that the piece needs rotating counter-clockwise. Hold the cube so that this piece is in the URF location, and apply R' D' R D R' D' R.
Corner piece on D face. Rotate D face so that the corner piece you want to move into position is directly underneath its intended location. If the corner piece has white (or whatever color you chose) on the bottom, and the destination of the piece is URF (i.e. the upper right hand corner on the front of the cube), apply R' D² R D R' D' R.
Corner piece on D face, and white side of the corner is on the left hand side, assuming that the piece is going to the URF location. Apply F D F'.
Corner piece on D face, and white side of the corner is on the right hand side, assuming that the piece is going to the URF location. Apply R' D' R.

You should be finished the white face by now. This step is fairly intuitive, so it shouldn't have been too much of a problem.

Step 2 -- Do the middle layer edge pieces

Okay, so the U face is done...Now we have to get the edge pieces of the middle layer in place, that is the FR, FL, BR, BL pieces.

There are four possibilities:

Edge piece is in the correct place and oriented correctly -- do nothing.
Edge piece is in correct place, but oriented incorrectly. In this case, you have to replace it with another piece temporarily. Choose an edge piece that is on the D face, and move it to the position of the aforementioned edge piece using the move described in the following list item.
Edge piece is in an incorrect place in the middle layer. In most cases, you can just skip this edge piece for now, as it will move to the D face when you put the correct edge piece in that place. If you have two edge pieces in the middle layer that are in each other's correct places, then you will need to break the cycle by replacing one of those edge pieces with one of the D face edge pieces.
Edge piece is on the D face. This is good. Let's say you want to move the yellow-red edge piece into place on the middle layer. (Your cube may not have yellow and red as adjacent pieces, so you may have to substitute different colors). Check which side of the yellow-red piece is actually on the D face. Say yellow is on the D face. Rotate the D face so that the yellow-red piece is opposite from the yellow center. (If the yellow center is on the F face, then the yellow-red piece is the DB piece, got it?). Now, hold the cube so that white is the U face, and the yellow center is on the F face. Which side of the yellow-red piece is the red face on? If the red center is on the L face, then apply F' D' F D L D L'. If the red center is on the R face, then apply F D F' D' R' D' R. One way to think about this move, if you're trying to memorize it, is that you are removing the corner piece on the U side right above the edge piece you're trying to replace, and then putting it back in from the other direction, with the side effect of moving the edge piece into the correct place.

This will have to be repeated at least 4 times in order to get all of the 4 middle layer edge pieces into place.

Step 3 -- Form cross on last layer

The first two layers should now be completely correct. From now on, turn the cube upside-down, so that the first face (white, in my example) is the D face. It will remain this way until the cube is complete. The reason for this is just to make the manipulations a bit easier to perform.

On my cube, green is opposite to white, so I will refer to the green face as being the new U face for our purposes. We must now try to form a green cross, out of the green center, and the four edge pieces that surround it.

There are 4 possibilities:

All four pieces are correct, and you have green cross on the U face. Do nothing.
Two adjacent edge pieces are correct. For example, the UF and UR piece have green on the top, forming a sort of L shape, with the center. The UL and UB pieces do not have green on the top. In this situation, hold the cube so that the UF and UR pieces have green on the top (as in the example earlier in this paragraph), and apply B U L U' L' B'.
Two opposite edge pieces are correct, and the other two aren't. Let's say UR and UL are correct (this should make a green line down the middle of the U face). Apply B L U L' U' B'.
No edge pieces have green on the top. Hold the cube any way (still keeping the green center on the top) and apply B L U L' U' B' F U R U' R' F' (for those of you who want to memorize the moves, you should realize that this is the same as doing the move in the third part of this section, then rotating the cube 180 degrees, and then applying the move in the second part of this section).

You should now have the bottom two layers all correct, as before, and a green cross (or whatever the color on your cube whose center is opposite to white is) on the top face.

IMPORTANT: If the bottom two faces are perfectly correct, and you have 1 or 3 edge pieces that show green on the top, then your cube is messed up. Somebody (maybe you!) took it apart (or changed the stickers around) at some point in time. Might as well take it all apart right now, reassemble it correctly and start again.

Step 4 -- Rotate U face edge pieces

You now have a green cross on the U face, but...these edge pieces may not be in the correct order. This step involves rotating them so that the can be lined up with their respective colors.

If all 4 pieces are correct (the entire cube is correct except for four corner pieces on the top layer), then do nothing.
If 1 piece is correct, then rotate the whole cube so that this piece is in the UL position (make sure green is still on the top). If the remaining 3 edge pieces need to be rotated clockwise, apply R² D' U² R' L F² R L' D R². If the pieces need to be rotated counter-clockwise, apply R² D' R' L F² R L' U² D R².
If 2 "adjacent" edge pieces (by "adjacent" here I mean pairs such as UF and UL, or UB and UL, and not UF and UB, or UR and UL), then rotate the U face so that only 1 edge piece is correct, and follow that rule.
If 2 opposite (i.e. not adjacent!) edge pieces are correct, then apply U or U' and follow the rule for 0 edge pieces correct.
If 0 edge pieces are correct, turn the U face so that: for the UF piece (which can be any piece), the F side of that piece is the same color as the R face center. Now apply R² D² B² D L² F² L² F² L² F² D' B² D² R².

The four U face edge pieces should now be in the correct place. The cube should be all correct now except for the four corner pieces on the U face.

Step 5 -- Position U face corner pieces

Now we must move the corner pieces into the right places.

There are 3 possibilities:

All 4 corner pieces are in the right place, although not necessarily rotated correctly. Do nothing.
1 corner piece is in the right place. Hold the cube so that it is in the UFR position. If the remaining three corner pieces need to be rotated clockwise, apply L' U R U' L U R' U'. If they need to be rotated counter-clockwise, apply U R U' L' U R' U' L.
0 corner pieces are in the right place. If they all need to go to opposite corners, apply R' B² F R F' R' F R F' R' F R F' R' B² R. If they need to go to adjacent corners, hold the cube so that UFR and UFL pieces need swapping, and so do the UBR and UBL pieces. Apply B L U L' U' L U L' U' L U L' U' B'.

Okay, now all of the corner pieces should be in the right place. We're almost there!

Step 6 -- Rotate corner pieces

Hold the cube so that an incorrectly rotated corner piece is in the UFR position. If it needs to be rotated clockwise, apply F D F' D' F D F' D'. If it needs to be rotated counter-clockwise, apply D F D' F' D F D' F'. Now (and this is extremely important) turn the U face only, so that the next incorrectly rotated corner piece is in the UFR position. Apply one of the above moves, depending on which way it needs rotating. Repeat if more than two corner pieces are incorrectly rotated. After all pieces are rotated, simply turn the U face and complete the cube.

This step may be confusing, simply because after just one corner piece is rotated the cube is in quite serious disarray. Just make certain that you move only the U face and it should work out fine. I'll give one example to show exactly what will happen, for a simple example: the UFR piece needs rotating clockwise, and the UBR piece needs rotating counter-clockwise. Do these moves and the cube will be complete F D F' D' F D F' D' U D F D' F' D F D' F' U'.

Note that there are only certain combinations of incorrectly rotated pieces. If your cube gets to a position where there is a situation other than one of these, then it has probably been taken apart by small green aliens, so I would recommend disassembling it and starting over.

One piece needs rotating clockwise, one piece needs rotating counter-clockwise, other two are correct.
Three pieces all need rotating clockwise, other one is correct.
Three pieces all need rotating counter-clockwise, other one is correct.
Two pieces need rotating clockwise, two pieces need rotating counter-clockwise.
I was going to write "all corner pieces are correct" here, but I guess that would be obvious.