Here's a picture of the mechanism:
Frankly, if I were going to try and build one from scratch, I'd go with the above mechanism rather than the modified 3x3x3. The pictures of the Octahedrons and Octahedron pieces you saw in the articles section are a custom built moulding of the above mechanism by Wayne.
But since you asked, this is my understanding of how to build one from a 3x3x3. The six corner pieces on the Octahedron are the centers of the 3x3x3. The twelve "edge" pieces on the Octahedron (the only ones that actually can move from position to position) are the edge cubies of the 3x3x3. Then you have the problem of the non-twisting trivial tips.