I'm going to be using a GTX 560 for audio, and was wondering, does this card have built-in audio, and if so, how would I use headphones with it? Or, should I just use the onboard sound on my motherboard?
A GeForce GTX 560 Ti does not have built-in audio. It only has HD Audio pass-through on its HDMI port.
Just use the motherboard's onboard audio because that is what gets passed through the HDMI port.