I haven't found much information about Celebi Machines, even after searching through the Internet for the last couple months, but this is some of the more notable information that I have gathered:
There is a (possibly modified) Super Famicom inside, which has a (also possibly modified) Super Gameboy 2 inserted in it.
Inside the SGB2 is a modified Gold version(or Blue for the Mew machines).
The SGB2 is connected to a modified Gameboy/Gameboy Color, which in most pictures you can see as the "IN" slot.
There is a glitch relating to Pokemon in the party having mail.
What I don't know:
If the Super Famicom/SGB2 is modified
How they are modified.
How the Pokemon Gold/GBC is modified
How the Celebi is distributed. I have heard that it is automatic, but that might be untrue.
These are merely my findings on this topic. I would love to hear everyone else's finds into this, whether it is false or true.