G4 Minis have no optical output connector for sound, only a stereo headphone jack. That makes the sound hookup very simple - just use an adapter cable with a headphone jack on one end and two RCA connectors (red and white) on the other end. Obviously, you only get stereo from this hookup, and no surround sound options.
How you hook it up to your TV depends a lot on the available inputs on your TV. If your TV has a DVI, HDMI, or VGA input, just get the appropriate cable.
Tilman