The octahedron can be made, as usual, in only one color.  However, it is more striking to build all of your models with parallel faces being of the same color.  The Octahedron will need 4 colors.  You must cut two triangles of each color.

Assemble each of the four color faces into one octahedron corner by gluing one edge at a time.  Once you have one corner completed you should be able to see where to apply the next color face because it should be parallel to the face with its like color.

Again, the last piece should be applied with one edge connected like the hinge of the top to a box.  Once that edge is dry, the remaining 2 edges should be glued at the same time and then lowered and held in place until the glue dries.

octahedron template:      triangle