This site has some really good pictures - http://pokemoncenternewyork.weebly.com/gaming-distribution-events.html
For the visitor, you would put your game (Gold, Silver, or Crystal) into the machine. There was a cartridge slot. You would get a cool video showing what Pokemon you got (or just an egg).
From my understanding and memory, the distributions were powered by Gamecubes (specifically development units, they were green when they opened the machines). Changing the distribution involved switching the disc that was in the Gamecube. They would sometimes switch the disc for special circumstances (far out of town visitor wanting Celebi) and sometimes might forget to put the disc into all four units. Another somewhat common occurrence was the machines would accidentally delete the save file. In this case, staff would bribe you with some shiny event Pokemon and additional eggs.
Each week a hidden tag was put in your game, so you couldn't repeat an event. There were ways around it. I think I used something called a "Monster Brain" and if the staff forgot to switch all the machines, hopping between the two machines seemed to suffice.
When examining Pokemon data, keep in mind some of them have been leveled up and not all of them may have come from the Crystal game, Zubat certainly came from Crystal. The battery on my brother's game failed earlier than the Crystal.