I have my Xbox connected to my computer monitor.
its an LG from, about...3 years ago now.
It has VGA (to my computer) and a DVI port. I was lucky in that I had recieved a HDMI to DVI MALE cable with my Star Choice Reciever. I plug the HDMI into the xbox and then the DVI into my monitor.
With my xbox I had also recieved a audio connection. It sits above the HDMI port on the back of the xbox and I plug in there.
I also have the X1 and with mine came a AUDIO to 3mm jack. From the Audio connection from the xbox I attach this adapter that will convert left and right audio to a 3 mm (I believe) jack. I then plug my Headphones into the jack and I have audio through my turtle beach headset....WHICH i love btw, best set of headphones I've EVER bought.
Does that give you more of an idea how it works?