Being a screenprinter I could not resist answering your question. I have never seen how discs are printed in production, but I know the basics about it.
If it is a photolike print, then you need a lot of things. First you need the original picture (not a scanned image or downloaded image. If you use that you are bound to get moare.(which is unwanted patterns in the image))
The image needs then to get separated into four color channels, CMYK (C= cyan M= magenta Y= yellow K=black) which is quite costly.
Then you need four screens with the correct meshcount.
Now you need to process these screen along with a film you received from the guys who made the colorseparation.
This is done in a light with a special wavelength, IÂ´m using a special halogenlight.
Then you need to mount the screens in a specialmachine which I dont know the english name of. However that machine is needed so the screens register exactly against eachother everytime.
When you have made the registration correct it is only to put each process ink on the correct screen and print away!
You probably gave the whole idea away at an early stage while reading this, I just wanted to give an insight how complicated this is. But in reality it is even more complicated then what I described.