"Marc, you need to connect the sat box's composite AV outs to the LG's composite inputs. These are the yellow/red/white RCA jacks."
Sorry, that's only step one. You'll also want to hook up the LG to the receiver and the TV by the best means possible. For audio you need one of the LG's digital audio outputs going into the receiver. For video, component (red/green/blue) into the receiver. That's assuming you are connecting the TV via the receiver's component outputs.
Do I keep the Component connections from the Satellite to the Receiver? My feeling is that if I want to have the best picture available, I should be using Component (my HDTV supports component but no HDMI).
"Do I keep the Component connections from the Satellite to the Receiver?"
Yes. The best input available on the LG recorder is the yellow/red/white composite. The ExpressVu receiver should feed its component video signal as usual through the Yamaha which feeds the TV. Meanwhile, the satbox will also feed its composite signal into the LG. The LG should then record whatever channel is tuned in at the time. It will not be possible to watch one channel while recording another simultaneously.
Then we've got to get the video from the LG to the TV, either by going through the Yamaha or by going directly to the TV. HDMI aside, the best way is component.
The audio from the LG has to be dealt with as well. The best hookup as I said above would be either the optical or coax digital outputs into the Yamaha.