The First challenge is How to turn
the Cube.
Now, let's use some basic logic in solving the Skewb.
Turns will be described by arrows where an arrow always means a turn by one "click" (120 degrees)
Applying any operation, this square always stays on the top. 
A turn of the whole cube by 90 degrees will be described by:


1. Solving the top
This is the first correctly set roof corner. 

We want to now set this roof corner. 
In order to set the right front roof corner look for the roof corner with the color. Bring it up in front to the right.
If it still needs to be orientated i.e. if its roof color is not yet on top  turn the cube so that this corner is at the back, and its roof color points either to the left or to the right, e.g.:




2. Setting the squares
It is a fact for all combinatorial games a strategy of solution is never uniquely determined. There are always many completely different methods for proceeding. Also here, with the Skewb we now could continue by setting the floor corners, but I found, that it is faster to do the squares first.
This color must show up here 
Now we want to set the squares. Their position is uniquely determined by the roof corners.
The Squares in the left and the back face don't move!





The Squares in the right and the back face don't move!





3. Orientation of the floor corners
This cube has a very charming quality: If the roof is complete, the four floor corners are correctly placed and only have to be orientated. There are only two cases: If all four corners have to be orientated turn the cube so that no floor color is in the front face:





If only two corners have to be orientated turn the cube so that one floor color is to the front right.









