From the photos I see two devices:

1. A Sony TV (presumably a Trinitron model).
2. A Pioneer DVD/CD Receiver

In the picture I can see that the Pioneer receiver only accepts one audio input.

What you can do in the setup is that you can plug the Red/White (Audio) cable of your PS3 to the audio input in your Pioneer receiver, leave the Yellow cable (Video) at the front panel of your TV. I assume that the picture output from the PS3 will be displayed in Video 2 of your TV. The PS3 portion is done.

Next, you would want to connect the video output of your DVD player to your TV. Take the Yellow cable from your DVD player and connect it to the back of your TV Yellow A/V Input. The picture output from your DVD player should be displayed in Video 1 of your TV.

There will be no audio connection from your DVD player to the receiver because the DVD player IS the receiver itself.

I believed that everytime you're switching from PS3<->DVD and vice versa, you would want to ensure that your Pioneer receiver will output the correct audio channel. Refer to your manual on how to do it. Otherwise, you won't hear any sound out of your PS3.

I hope this clarifies your confusion.

Cheers