How to solve the Skewb
The Skewb was inveted by Tony Durham and is quite different to the Rubik's cube. There are no centre pieces which do not move on this piece so to work out which side is opposite which you will have to examine the corner pieces. On top of that every twist will effect each of the six faces of the Skewb.
Notation
In a similar, but different, style to the Rubik's cube we label moves by the corner at the centre of the twist. For example, FLD means turn clockwise around the "front-left-down" corner. Take some time to understand how this works. The pictures below show the corner to turn around (in grey) and then what that looks like after it's performed.
FLD = "front-left-down"
Result
FRD = "front-right-down"
Result
BLD = "back-left-down"
Result
BRD = "back-right-down"
Result
Step 1
Aim
Get the corners into place using intuition. You should be able to get three in place yourself and then the final corner may need rotating. Get this corner into the FLU position and use the following algorithm to rotate it clockwise.
Algorithm: FLD' BLD' FLD BLD
This algorithm will rotate it anti-clockwise:
Algorithm: FLD FRD FLD' FRD'
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Step 2
Aim
This step involves getting the large center pieces into place. Keep your solved face (in these pictures this is the White face) as the Up face. This algorithm will rotate the centers that are touching the FRD corner piece in a clockwise fashion.
Algorithm: FLD BLD FLD' BLD' BRD' BLD' BRD BLD
Alternatively to rotate the centre pieces around the FLD corner piece ant-clockwise use this algorithm:
Algorithm: FRD' BRD' FRD BRD BLD BRD BLD' BRD
Step 3
Aim
Now to put the final corners into place and then you're done with this How to solve the Skewb guide! Keep your first solved face as the up face and use the following to move the corners. If you have two corners that have the same colour on the left/right/front/back side then put those two in the back! If not keep using this algorithm until some appear.
Algorithm: FRD' BRD FRD BRD' FRD' BRD FRD BRD'