The title here is slightly misleading- this isn't how LEDs are made, it is how LED dies are packaged. The more difficult part of all of this is creating the dies themselves, which is requires a clean room and all the automated tools I'm sure most people here were expecting to see.
and a lab to get a better feel for how band gaps affect the spectrum: http://electron6.phys.utk.edu/phys250/Laboratories/Light%20e...