If the tutorial in question says you need 24 normals, that probably means you need to "explode" the cube into 6 non-connected polygons. You can do this in Blender by tabbing into edit mode for the cube, choosing edge selection, selecting all, and using Mesh -> Edges -> Edge Split. That way you get 4*6 = 24 vertices and you should now have 24 vertex normals as well. Looking at the vertex normals now, you have 3 normals at each corner because they are now 3 separate vertices. The vertex normal that was previously [1,1,1] is now 3 normals [1,0,0], [0,1,0] and [0,0,1] so it's been divided into components for each of the 3 faces.
Your solution seems to work. This is how I do it.
Take the predefined Cube which has only 6 faces, 8 vertices and 8 normals at first.
Now I go to Mesh->Faces->Triangulate Faces. This is because I need the faces to be triangles.
Now Mesh->Edges(with all edges selected)->Edge Split
Well this actually does the trick. Now I have 12 faces and normals for each vertex which look right to me. The problem is, in the entire process somehow more vertices were generated. I end up with 36 vertices. I can't see them. Tried to go to Mesh->Vetrtices->Remove Duplicates. But this deletes the normals and even the edges I created with triangulation.