The icosahedron will have 20 faces made of 5 colors.
You will need to create 4 faces of each color. In contrast to the other Platonic Solids, this figure will not exhibit parallel faces of the same color.
Begin assembling your shape by assembling five faces (one of each color) into a pentagonal pyramid that you can see in the picture above. Place your 6th triangular face directly across and slightly to the right from the face in the initial pyramid of the same color. Add the next 4 triangle faces in the same way.
Now, by tilting that original pentagonal pyramid, consider where the next such pyramid will be. That pyramid is missing only one color face and now you can glue that face into place. Continue in this manner to complete all of the the pyramids that complete the icosahedron.
To see the full sized template click on this image: