I plugged the audio cable into the internal AUX input on my motherboard. That was all I had to do. Now I'm hearing all that 8-bit goodness coming out of my speakers. It's great!
I switched the SID chips around so that chip #1 is the one that came from the C-64 I had lying around. I got it from my high school way back when, when they were switching over to another platform and that one had a broken keyboard. That way I get to hear it play with the current CW drivers.