This is a simple 3 step solution to solving the Skewb Diamond (4-axis Octahedron)
I try to go slowly and explain each step as clearly as possible. There are notes in the margin for you to follow along.
Here are those notes:
Solve the corners:
match the whites
match the yellows: R U' R' U (F)
Solve the centers:
center swap: R U' R' U (x3)
3 piece cycle: R U' R' U' R U' R' U'
Hope this helps you!
If anything is unclear please let me know in the comments.