It sounds like you have the AM-FM Multiplex radio. It's basically a radio that lets you listen to FM stereo broadcasts. The green, black and violet colored wires are the audio outputs. They feed to the stereo switch and crossover.
The FSM will show you where those wires go.
There should be a red wire for power and an orange wire for the light. No ground wire.
I was curious, so I went to the "out of site" web site. If you just have the radio, and don't have the other components (stereo switch and crossover), then I don't think this is going to work as well as you hoped. The best way would be to use the speaker wires coming out of the crossover and hook those to the inputs. Since it's "high level" output, don't expect much.
But it sounds like you don't have the crossover and stereo switch, so you may be able to use the green wire for one channel and violet wire for the other... ground for the - side of each channel... but I'm not sure. I would expect it not to sound very good either.
It pretty much comes down to the radio and sound system in the car has to be complete and working before you add something like this.
If you are stuck with this piece, it might be worth sourcing a regular AM-FM radio.... Or just play music from your I-phone or whatever and skip any input from the radio.
You'll really hate to hear this... but for a few bucks more, you could have just had the existing radio upgraded so you wouldn't need the "out of sight" stuff.
AM/FM Stereo Conversions for old car radios