The
Skewb is a cubic twisty puzzle invented by Tony Durham and mass marketed by Uwe Meffert and his company,
Meffert's Puzzles. The Skewb has 6 faces and, unlike the faceturning Rubik's Cube, is a vertexturning puzzle, which results in a very different type of challenge. There are a number of approaches to solving the Skewb. The following solution most closely resembles the one published by Meffert's and packaged with the puzzle.
Acknowledgement
Special thanks to Gelatinbrain, who has graciously given permission for Twistypuzzles.com's published solutions to utilize screen shots from his excellent puzzle simulator. Gelatinbrain's Skewb simulator may be found here.
Notation
Each of the six faces of the cube will be referred to by its position on the cube, as shown here:
Opposite the faces shown in the picture, we will have the D, L, and B faces (Down, Left, and Back). To denote a twist of the puzzle, we will identify the vertex (corner) to be twisted by the faces it touches, therefore, a clockwise twist of the corner touching the Up, Front, and Right faces will be notated as UFR. A counterclockwise twist of the same corner will be notated as UFR'. The result of a UFR twist on a solved cube is illustrated below:
The remaining six corners will be identified as UFL, DFL, DFR, UBL, UBR, DBL, and DBR.
Step 1 – Top Corners
To begin solving the Skewb, we must first choose which color will be represented on the top face. For our purposes, white will be the top color. Not all physical cubes have a white side, however, which does not matter. Choose a color you are comfortable with.
Locate the center which belongs on the top face and turn the cube in your hands so that center is, in fact, located on the top face, as shown:
One or more of the corresponding top corners may be correctly positioned and oriented. If all top corners are located in the bottom corner positions, then perform a DFR twist, which should move one top corner to the top face. Once one corner is correctly positioned on the top face, that vertex will be our starting point for solving the rest of the top corners.
If the first top corner is correctly positioned, but is not correctly oriented, rotate the cube in your hands so that corner is in either the UFL or UFR position, with the top color on the F face.
If the corner is in the UFL position, perform the following sequence of moves:
DFR, DFL, DFR', DFL'
This sequence will rotate the UFL corner counterclockwise, bringing the top color to the top face:
If the corner to be rotated is in the UFR position as shown below,
perform the following sequence:
UFL', UFR', UFL, UFR
This sequence will rotate the UFR corner clockwise, bringing the top color to the top face.
At this point one top corner is correctly positioned and oriented. The remaining top corners can all be positioned and oriented using the steps listed above. You must pay attention when using DFR to move the corners to the top layer that the other colors on the corners in question match up. For example, in the above picture, the other white/blue corner must be moved to the UFL position. The other top corners will not be disturbed by these sequences.
If a top corner is in the top layer, but out of position, rotate the cube until that corner is in the UFR position and perform a DFR twist. This will move the corner in to the bottom layer and allow for movement to the proper position.
When the top corners are correctly positioned and oriented, the Skewb should look similar to this:
You may now move on to Step 2.
Step 2 – Remaining 5 Centers
Now that the top center and corners are solved, we will work on the remaining centers. These can be solved with a pair of opposite 3center cycles.
To cycle the centers from F→L→D→F, perform the following sequence:
DFR', DBR', DFR, DBR, DBL, DBR, DBL', DBR'
To cycle the centers from F→R→D→F, perform the following sequence:
DFL, DBL, DFL', DBL', DBR', DBL', DBR, DBL
Performing this sequence on our sample cube pictured above with blue as the front face will result in this:



Front View 

Opposite View 
As you can see, only one more center 3cycle is require to solve the remaining centers. You should be able to solve all centers using the above 3cycles no more than twice.
When all centers are solved, you may move on to Step 3.
Step 3 – Bottom Corners
Now that the top corners and all centers are solved, we are left with the bottom corners. If you have made it to this point, you will notice that all of the bottom corners are already correctly positioned, and all that remains is to orient them. There are two possible cases:
Case 1: Two bottom corners are incorrectly oriented:
If you find yourself in Case 1, rotate the cube in your hands until you have an incorrectly oriented corner in the DFR position which needs to be rotated counterclockwise, as shown above. Perform the following sequence:
[DFR', DBR, DFR, DBR'] x2, [DFL', DFR, DFL, DFR'] x2
Case 2: All four bottom corners are incorrectly oriented:
If you find yourself in Case 2, look at the bottom of the cube. Two of the bottom corners will be rotated so that they show the same, incorrect, color, as shown above. Rotate the cube in your hands until those two corners occupy the DFL and DFR positions. Then perform the following sequence:
[DFR', DBR, DFR, DBR'] x2
The Skewb is now solved. Congratulations!
This solution can be used as a basis for tackling more challenging puzzles such as the Skewb Ultimate, Master Skewb, and Tony Fisher's Golden Cube.